Society for Industrial and Applied Mathematics: SIAM Journal on Financial Mathematics: Table of Contents
Table of Contents for SIAM Journal on Financial Mathematics. List of articles from both the latest and ahead of print issues.
https://epubs.siam.org/loi/sjfmbj?ai=s8&mi=3f5qtr&af=R
Society for Industrial and Applied Mathematics: SIAM Journal on Financial Mathematics: Table of Contents
Society for Industrial and Applied Mathematics
en-US
SIAM Journal on Financial Mathematics
SIAM Journal on Financial Mathematics
https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg
https://epubs.siam.org/loi/sjfmbj?ai=s8&mi=3f5qtr&af=R
-
Order Book Queue Hawkes Markovian Modeling
https://epubs.siam.org/doi/abs/10.1137/22M1470815?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 1-25, March 2024. <br/> Abstract. This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classified intraday order book trading events into a range of categories based on their order types and the price change after their arrivals. In order to capture the stimulating effects between multiple types of order book events, we use a multivariate Hawkes process to model the self-exciting and mutually exciting event arrivals. We also integrate Markovian baseline intensities into the event arrival dynamic, by including the impacts of order book liquidity state and time factor on the baseline intensity. A regression-based nonparametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated into the estimation procedure. Besides, a model selection method based on Akaike information criteria is applied to evaluate the effect of each part of the proposed model. An implementation example based on real limit order book data is provided. Through the example we studied the empirical shapes of Hawkes excitement functions, the effects of liquidity as well as time factors, the LASSO variable selection, and the explanation power of Hawkes and Markovian elements to the dynamics of order book.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 1-25, March 2024. <br/> Abstract. This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classified intraday order book trading events into a range of categories based on their order types and the price change after their arrivals. In order to capture the stimulating effects between multiple types of order book events, we use a multivariate Hawkes process to model the self-exciting and mutually exciting event arrivals. We also integrate Markovian baseline intensities into the event arrival dynamic, by including the impacts of order book liquidity state and time factor on the baseline intensity. A regression-based nonparametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated into the estimation procedure. Besides, a model selection method based on Akaike information criteria is applied to evaluate the effect of each part of the proposed model. An implementation example based on real limit order book data is provided. Through the example we studied the empirical shapes of Hawkes excitement functions, the effects of liquidity as well as time factors, the LASSO variable selection, and the explanation power of Hawkes and Markovian elements to the dynamics of order book.
Order Book Queue Hawkes Markovian Modeling
10.1137/22M1470815
SIAM Journal on Financial Mathematics
2024-01-30T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Philip E. Protter
Qianfan Wu
Shihao Yang
Order Book Queue Hawkes Markovian Modeling
15
1
1
25
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M1470815
https://epubs.siam.org/doi/abs/10.1137/22M1470815?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Exploratory Control with Tsallis Entropy for Latent Factor Models
https://epubs.siam.org/doi/abs/10.1137/22M153505X?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 26-53, March 2024. <br/> Abstract. We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis entropy and derive the optimal distribution over states—which we prove is [math]-Gaussian distributed with location characterized through the solution of an BS[math]E and BSDE in discrete and continuous time, respectively. We discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution. Finally, we develop the optimal policy in a model-agnostic setting along the lines of soft [math]-learning. The approach may be applied in, e.g., developing more robust statistical arbitrage trading strategies.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 26-53, March 2024. <br/> Abstract. We study optimal control in models with latent factors where the agent controls the distribution over actions, rather than actions themselves, in both discrete and continuous time. To encourage exploration of the state space, we reward exploration with Tsallis entropy and derive the optimal distribution over states—which we prove is [math]-Gaussian distributed with location characterized through the solution of an BS[math]E and BSDE in discrete and continuous time, respectively. We discuss the relation between the solutions of the optimal exploration problems and the standard dynamic optimal control solution. Finally, we develop the optimal policy in a model-agnostic setting along the lines of soft [math]-learning. The approach may be applied in, e.g., developing more robust statistical arbitrage trading strategies.
Exploratory Control with Tsallis Entropy for Latent Factor Models
10.1137/22M153505X
SIAM Journal on Financial Mathematics
2024-02-05T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Ryan Donnelly
Sebastian Jaimungal
Exploratory Control with Tsallis Entropy for Latent Factor Models
15
1
26
53
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M153505X
https://epubs.siam.org/doi/abs/10.1137/22M153505X?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures
https://epubs.siam.org/doi/abs/10.1137/22M152894X?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 54-92, March 2024. <br/> Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is equivalent to a problem of maximizing a weighted average of constant-absolute-risk-aversion certainty equivalents. The solutions of all the optimization problems are explicitly characterized, and an iterative method is provided to obtain the solutions numerically.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 54-92, March 2024. <br/> Abstract.A risk measure that is consistent with the second-order stochastic dominance and additive for sums of independent random variables can be represented as a weighted entropic risk measure (WERM). The expected utility maximization problem with risk controlled by WERM and a related risk minimization problem are investigated in this paper. The latter is equivalent to a problem of maximizing a weighted average of constant-absolute-risk-aversion certainty equivalents. The solutions of all the optimization problems are explicitly characterized, and an iterative method is provided to obtain the solutions numerically.
Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures
10.1137/22M152894X
SIAM Journal on Financial Mathematics
2024-02-27T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jianming Xia
Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures
15
1
54
92
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M152894X
https://epubs.siam.org/doi/abs/10.1137/22M152894X?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Multidimensional Kyle–Back Model with a Risk Averse Informed Trader
https://epubs.siam.org/doi/abs/10.1137/21M1457059?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 93-120, March 2024. <br/> Abstract. We study the continuous time Kyle–Back model with a risk averse informed trader. We show that in a market with multiple assets and non-Gaussian prices an equilibrium exists. The equilibrium is constructed by considering a Fokker–Planck equation and a system of partial differential equations that are coupled with an optimal transport type constraint at maturity.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 93-120, March 2024. <br/> Abstract. We study the continuous time Kyle–Back model with a risk averse informed trader. We show that in a market with multiple assets and non-Gaussian prices an equilibrium exists. The equilibrium is constructed by considering a Fokker–Planck equation and a system of partial differential equations that are coupled with an optimal transport type constraint at maturity.
Multidimensional Kyle–Back Model with a Risk Averse Informed Trader
10.1137/21M1457059
SIAM Journal on Financial Mathematics
2024-03-14T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Shreya Bose
Ibrahim Ekren
Multidimensional Kyle–Back Model with a Risk Averse Informed Trader
15
1
93
120
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/21M1457059
https://epubs.siam.org/doi/abs/10.1137/21M1457059?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum
https://epubs.siam.org/doi/abs/10.1137/22M149212X?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 121-160, March 2024. <br/> Abstract. This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the nonnegative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual-transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in piecewise closed form, and some thresholds of the wealth variable are obtained. The optimal consumption and investment control can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 121-160, March 2024. <br/> Abstract. This paper studies an optimal consumption problem for a loss-averse agent with reference to past consumption maximum. To account for loss aversion on relative consumption, an S-shaped utility is adopted that measures the difference between the nonnegative consumption rate and a fraction of the historical spending peak. We consider the concave envelope of the utility with respect to consumption, allowing us to focus on an auxiliary HJB variational inequality on the strength of concavification principle and dynamic programming arguments. By applying the dual-transform and smooth-fit conditions, the auxiliary HJB variational inequality is solved in piecewise closed form, and some thresholds of the wealth variable are obtained. The optimal consumption and investment control can be derived in the piecewise feedback form. The rigorous verification proofs on optimality and concavification principle are provided. Some numerical sensitivity analysis and financial implications are also presented.
Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum
10.1137/22M149212X
SIAM Journal on Financial Mathematics
2024-03-15T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Xun Li
Xiang Yu
Qinyi Zhang
Optimal Consumption with Loss Aversion and Reference to Past Spending Maximum
15
1
121
160
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M149212X
https://epubs.siam.org/doi/abs/10.1137/22M149212X?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
A Multi-agent Targeted Trading Equilibrium with Transaction Costs
https://epubs.siam.org/doi/abs/10.1137/22M1542982?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 161-193, March 2024. <br/> Abstract. We prove the existence of a continuous-time Radner equilibrium with multiple agents and transaction costs. The agents are incentivized to trade towards a targeted number of shares throughout the trading period and seek to maximize their expected wealth minus a penalty for deviating from their targets. Their wealth is further reduced by transaction costs that are proportional to the number of stock shares traded. The agents’ targeted number of shares are publicly known. In equilibrium, each agent optimally chooses to trade for an initial time interval before stopping trade. Our equilibrium construction and analysis involves identifying the order in which the agents stop trade. The transaction cost level impacts the equilibrium stock price drift. We analyze the equilibrium outcomes and provide numerical examples.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 161-193, March 2024. <br/> Abstract. We prove the existence of a continuous-time Radner equilibrium with multiple agents and transaction costs. The agents are incentivized to trade towards a targeted number of shares throughout the trading period and seek to maximize their expected wealth minus a penalty for deviating from their targets. Their wealth is further reduced by transaction costs that are proportional to the number of stock shares traded. The agents’ targeted number of shares are publicly known. In equilibrium, each agent optimally chooses to trade for an initial time interval before stopping trade. Our equilibrium construction and analysis involves identifying the order in which the agents stop trade. The transaction cost level impacts the equilibrium stock price drift. We analyze the equilibrium outcomes and provide numerical examples.
A Multi-agent Targeted Trading Equilibrium with Transaction Costs
10.1137/22M1542982
SIAM Journal on Financial Mathematics
2024-03-21T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jin Hyuk Choi
Jetlir Duraj
Kim Weston
A Multi-agent Targeted Trading Equilibrium with Transaction Costs
15
1
161
193
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M1542982
https://epubs.siam.org/doi/abs/10.1137/22M1542982?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Deep Signature Algorithm for Multidimensional Path-Dependent Options
https://epubs.siam.org/doi/abs/10.1137/23M1571563?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 194-214, March 2024. <br/> Abstract. In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [C. Huré, H. Pham, and X. Warin, Math. Comp., 89 (2020), pp. 1547–1579] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems, while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided, including Amerasian option under the Black–Scholes model, American option with a path-dependent geometric mean payoff function, and Shiryaev’s optimal stopping problem.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 194-214, March 2024. <br/> Abstract. In this work, we study the deep signature algorithms for path-dependent options. We extend the backward scheme in [C. Huré, H. Pham, and X. Warin, Math. Comp., 89 (2020), pp. 1547–1579] for state-dependent FBSDEs with reflections to path-dependent FBSDEs with reflections, by adding the signature layer to the backward scheme. Our algorithm applies to both European and American type option pricing problems, while the payoff function depends on the whole paths of the underlying forward stock process. We prove the convergence analysis of our numerical algorithm with explicit dependence on the truncation order of the signature and the neural network approximation errors. Numerical examples for the algorithm are provided, including Amerasian option under the Black–Scholes model, American option with a path-dependent geometric mean payoff function, and Shiryaev’s optimal stopping problem.
Deep Signature Algorithm for Multidimensional Path-Dependent Options
10.1137/23M1571563
SIAM Journal on Financial Mathematics
2024-03-22T07:00:00Z
© 2024 Erhan Bayraktar, Qi Feng, Zhaoyu Zhang
Erhan Bayraktar
Qi Feng
Zhaoyu Zhang
Deep Signature Algorithm for Multidimensional Path-Dependent Options
15
1
194
214
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/23M1571563
https://epubs.siam.org/doi/abs/10.1137/23M1571563?ai=s8&mi=3f5qtr&af=R
© 2024 Erhan Bayraktar, Qi Feng, Zhaoyu Zhang
-
Mild to Classical Solutions for XVA Equations under Stochastic Volatility
https://epubs.siam.org/doi/abs/10.1137/22M1506882?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 215-254, March 2024. <br/> Abstract. We extend the valuation of contingent claims in the presence of default, collateral, and funding to a random functional setting and characterize pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we relax conditions on the available market information and construct a broad class of default times. Moreover, under stochastic volatility, we characterize pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 215-254, March 2024. <br/> Abstract. We extend the valuation of contingent claims in the presence of default, collateral, and funding to a random functional setting and characterize pre-default value processes by martingales. Pre-default value semimartingales can also be described by BSDEs with random path-dependent coefficients and martingales as drivers. En route, we relax conditions on the available market information and construct a broad class of default times. Moreover, under stochastic volatility, we characterize pre-default value processes via mild solutions to parabolic semilinear PDEs and give sufficient conditions for mild solutions to exist uniquely and to be classical.
Mild to Classical Solutions for XVA Equations under Stochastic Volatility
10.1137/22M1506882
SIAM Journal on Financial Mathematics
2024-03-25T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Damiano Brigo
Federico Graceffa
Alexander Kalinin
Mild to Classical Solutions for XVA Equations under Stochastic Volatility
15
1
215
254
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/22M1506882
https://epubs.siam.org/doi/abs/10.1137/22M1506882?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Generalized Optimized Certainty Equivalent with Applications in the Rank-Dependent Utility Model
https://epubs.siam.org/doi/abs/10.1137/21M1448276?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 255-294, March 2024. <br/> Abstract. The classic optimized certainty equivalent (OCE), proposed by Ben-Tal and Teboulle [Manag. Sci., 11 (1986), pp. 1445–1466], employs the classical expected utility model to evaluate the random risk, in which model each decision maker is characterized by a unique probability measure and only outcome uncertainty is assumed. Due to the lack of information, the distribution ambiguity or Knightian uncertainty prevails in reality. We employ the variational preference of Maccheroni, Marinacci, and Rustichini [Econometrica, 74 (2006), pp. 1447–1498] to address the issue and generalize the concept of OCE. In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on [math]-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of the RDU-based shortfall risk measure proposed by Mao and Cai [Finance Stoch., 2 (2018), pp. 367–393] is also presented.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 255-294, March 2024. <br/> Abstract. The classic optimized certainty equivalent (OCE), proposed by Ben-Tal and Teboulle [Manag. Sci., 11 (1986), pp. 1445–1466], employs the classical expected utility model to evaluate the random risk, in which model each decision maker is characterized by a unique probability measure and only outcome uncertainty is assumed. Due to the lack of information, the distribution ambiguity or Knightian uncertainty prevails in reality. We employ the variational preference of Maccheroni, Marinacci, and Rustichini [Econometrica, 74 (2006), pp. 1447–1498] to address the issue and generalize the concept of OCE. In this paper, we introduce a class of optimized certainty equivalent based on the variational preference, give its dual representation based on [math]-divergence, and study its equivalent characterization of positive homogeneity and coherence. As applications, we investigate the properties of optimized certainty equivalent based on the rank-dependent utility (RDU) model. The dual representation of the RDU-based shortfall risk measure proposed by Mao and Cai [Finance Stoch., 2 (2018), pp. 367–393] is also presented.
Generalized Optimized Certainty Equivalent with Applications in the Rank-Dependent Utility Model
10.1137/21M1448276
SIAM Journal on Financial Mathematics
2024-03-26T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Qinyu Wu
Tiantian Mao
Taizhong Hu
Generalized Optimized Certainty Equivalent with Applications in the Rank-Dependent Utility Model
15
1
255
294
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/21M1448276
https://epubs.siam.org/doi/abs/10.1137/21M1448276?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Robust Portfolio Selection under Recovery Average Value at Risk
https://epubs.siam.org/doi/abs/10.1137/23M1555491?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page 295-314, March 2024. <br/> Abstract. We study mean-risk optimal portfolio problems where risk is measured by recovery average value at risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical average value at risk shows that portfolio selection under its recovery version enables financial institutions to exert better control on the recovery on liabilities while still allowing for tractable computations.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page 295-314, March 2024. <br/> Abstract. We study mean-risk optimal portfolio problems where risk is measured by recovery average value at risk, a prominent example in the class of recovery risk measures. We establish existence results in the situation where the joint distribution of portfolio assets is known as well as in the situation where it is uncertain and only assumed to belong to a set of mixtures of benchmark distributions (mixture uncertainty) or to a cloud around a benchmark distribution (box uncertainty). The comparison with the classical average value at risk shows that portfolio selection under its recovery version enables financial institutions to exert better control on the recovery on liabilities while still allowing for tractable computations.
Robust Portfolio Selection under Recovery Average Value at Risk
10.1137/23M1555491
SIAM Journal on Financial Mathematics
2024-03-29T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Cosimo Munari
Justin Plückebaum
Stefan Weber
Robust Portfolio Selection under Recovery Average Value at Risk
15
1
295
314
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/23M1555491
https://epubs.siam.org/doi/abs/10.1137/23M1555491?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?
https://epubs.siam.org/doi/abs/10.1137/23M1580413?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page SC1-SC14, March 2024. <br/> Abstract. Shortfall systemic (multivariate) risk measures [math] defined through an [math]-dimensional multivariate utility function [math] and random allocations can be represented as classical (1-dimensional) shortfall risk measures associated to an explicitly determined 1-dimensional function constructed from [math]. This finding allows for simplifying the study of several properties of [math], such as dual representations, law invariance, and stability.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page SC1-SC14, March 2024. <br/> Abstract. Shortfall systemic (multivariate) risk measures [math] defined through an [math]-dimensional multivariate utility function [math] and random allocations can be represented as classical (1-dimensional) shortfall risk measures associated to an explicitly determined 1-dimensional function constructed from [math]. This finding allows for simplifying the study of several properties of [math], such as dual representations, law invariance, and stability.
Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?
10.1137/23M1580413
SIAM Journal on Financial Mathematics
2024-01-04T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Alessandro Doldi
Marco Frittelli
Emanuela Rosazza Gianin
Short Communication: Are Shortfall Systemic Risk Measures One Dimensional?
15
1
SC1
SC14
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/23M1580413
https://epubs.siam.org/doi/abs/10.1137/23M1580413?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Short Communication: Optimal Insurance to Maximize Exponential Utility When Premium Is Computed by a Convex Functional
https://epubs.siam.org/doi/abs/10.1137/23M1601237?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/1">Volume 15, Issue 1</a>, Page SC15-SC27, March 2024. <br/> Abstract. We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.
SIAM Journal on Financial Mathematics, Volume 15, Issue 1, Page SC15-SC27, March 2024. <br/> Abstract. We find the optimal indemnity to maximize the expected utility of terminal wealth of a buyer of insurance whose preferences are modeled by an exponential utility. The insurance premium is computed by a convex functional. We obtain a necessary condition for the optimal indemnity; then, because the candidate optimal indemnity is given implicitly, we use that necessary condition to develop a numerical algorithm to compute it. We prove that the numerical algorithm converges to a unique indemnity that, indeed, equals the optimal policy. We also illustrate our results with numerical examples.
Short Communication: Optimal Insurance to Maximize Exponential Utility When Premium Is Computed by a Convex Functional
10.1137/23M1601237
SIAM Journal on Financial Mathematics
2024-03-08T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jingyi Cao
Dongchen Li
Virginia R. Young
Bin Zou
Short Communication: Optimal Insurance to Maximize Exponential Utility When Premium Is Computed by a Convex Functional
15
1
SC15
SC27
2024-03-31T07:00:00Z
2024-03-31T07:00:00Z
10.1137/23M1601237
https://epubs.siam.org/doi/abs/10.1137/23M1601237?ai=s8&mi=3f5qtr&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Cubature Method for Stochastic Volterra Integral Equations
https://epubs.siam.org/doi/abs/10.1137/22M146889X?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 959-1003, December 2023. <br/> Abstract. In this paper, we introduce the cubature formula for stochastic Volterra integral equations. We first derive the stochastic Taylor expansion in this setting, by utilizing a functional Itô formula, and provide its tail estimates. We then introduce the cubature measure for such equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model. We shall provide the error estimate rigorously. Our numerical examples show that the cubature method is much more efficient than the Euler scheme, provided certain conditions are satisfied.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 959-1003, December 2023. <br/> Abstract. In this paper, we introduce the cubature formula for stochastic Volterra integral equations. We first derive the stochastic Taylor expansion in this setting, by utilizing a functional Itô formula, and provide its tail estimates. We then introduce the cubature measure for such equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model. We shall provide the error estimate rigorously. Our numerical examples show that the cubature method is much more efficient than the Euler scheme, provided certain conditions are satisfied.
Cubature Method for Stochastic Volterra Integral Equations
10.1137/22M146889X
SIAM Journal on Financial Mathematics
2023-10-10T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Qi Feng
Jianfeng Zhang
Cubature Method for Stochastic Volterra Integral Equations
14
4
959
1003
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M146889X
https://epubs.siam.org/doi/abs/10.1137/22M146889X?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders
https://epubs.siam.org/doi/abs/10.1137/21M1443546?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1004-1027, December 2023. <br/> Abstract. We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free variational autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and Lévy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces. We further refine the VAE model by including conditional features and demonstrate its superior generative out-of-sample performance. Finally, we showcase how our method can be used as a data augmentation tool to help practitioners manage the tail risk of option portfolios.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1004-1027, December 2023. <br/> Abstract. We propose a hybrid method for generating arbitrage-free implied volatility (IV) surfaces consistent with historical data by combining model-free variational autoencoders (VAEs) with continuous time stochastic differential equation (SDE) driven models. We focus on two classes of SDE models: regime switching models and Lévy additive processes. By projecting historical surfaces onto the space of SDE model parameters, we obtain a distribution on the parameter subspace faithful to the data on which we then train a VAE. Arbitrage-free IV surfaces are then generated by sampling from the posterior distribution on the latent space, decoding to obtain SDE model parameters, and finally mapping those parameters to IV surfaces. We further refine the VAE model by including conditional features and demonstrate its superior generative out-of-sample performance. Finally, we showcase how our method can be used as a data augmentation tool to help practitioners manage the tail risk of option portfolios.
Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders
10.1137/21M1443546
SIAM Journal on Financial Mathematics
2023-10-11T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Brian (Xin) Ning
Sebastian Jaimungal
Xiaorong Zhang
Maxime Bergeron
Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders
14
4
1004
1027
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/21M1443546
https://epubs.siam.org/doi/abs/10.1137/21M1443546?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets
https://epubs.siam.org/doi/abs/10.1137/22M1527246?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1028-1061, December 2023. <br/> Abstract. We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sublinear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problems.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1028-1061, December 2023. <br/> Abstract. We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then apply this algorithm to a variety of energy scheduling problems, including novel high-dimensional energy production problems. Our experimental results demonstrate that the algorithm performs with accuracy and experiences linear to sublinear slowdowns as dimension increases, demonstrating the value of the algorithm for solving high-dimensional switching problems.
A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets
10.1137/22M1527246
SIAM Journal on Financial Mathematics
2023-10-16T07:00:00Z
© 2023 Erhan Bayraktar, Asaf Cohen, April Nellis
Erhan Bayraktar
Asaf Cohen
April Nellis
A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets
14
4
1028
1061
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1527246
https://epubs.siam.org/doi/abs/10.1137/22M1527246?ai=s8&mi=3f5qtr&af=R
© 2023 Erhan Bayraktar, Asaf Cohen, April Nellis
-
Interest Rates Term Structure Models Driven by Hawkes Processes
https://epubs.siam.org/doi/abs/10.1137/22M1502604?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1062-1079, December 2023. <br/> Abstract. This paper includes a marked Hawkes process in the original Heath–Jarrow–Morton (HJM) setup and investigates the impact of this assumption on the pricing of the popular vanilla fixed-income derivatives. Our model exhibits a smile that can fit the implied volatility of swaptions for a given key rate (tenor). We harness the log-normality of the model, conditionally with respect to jumps, and derive formulae to evaluate both caplets/floorlets and swaptions. Our model exhibits negative jumps on the zero-coupon (hence positive on the rates). Therefore, its behavior is compatible with the situation where globally low interest rates can suddenly show a cluster of positive jumps in case of tensions on the market. One of the main difficulties when dealing with the HJM model is to keep a framework that is Markovian. In this paper we show how to preserve the relevant features of the Hull and White version, especially the reconstruction formula that provides the zero-coupon bonds in terms of the underlying model factors.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1062-1079, December 2023. <br/> Abstract. This paper includes a marked Hawkes process in the original Heath–Jarrow–Morton (HJM) setup and investigates the impact of this assumption on the pricing of the popular vanilla fixed-income derivatives. Our model exhibits a smile that can fit the implied volatility of swaptions for a given key rate (tenor). We harness the log-normality of the model, conditionally with respect to jumps, and derive formulae to evaluate both caplets/floorlets and swaptions. Our model exhibits negative jumps on the zero-coupon (hence positive on the rates). Therefore, its behavior is compatible with the situation where globally low interest rates can suddenly show a cluster of positive jumps in case of tensions on the market. One of the main difficulties when dealing with the HJM model is to keep a framework that is Markovian. In this paper we show how to preserve the relevant features of the Hull and White version, especially the reconstruction formula that provides the zero-coupon bonds in terms of the underlying model factors.
Interest Rates Term Structure Models Driven by Hawkes Processes
10.1137/22M1502604
SIAM Journal on Financial Mathematics
2023-10-17T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Guillaume Bernis
Matthieu Garcin
Simone Scotti
Carlo Sgarra
Interest Rates Term Structure Models Driven by Hawkes Processes
14
4
1062
1079
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1502604
https://epubs.siam.org/doi/abs/10.1137/22M1502604?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
A Mean-Field Game of Market-Making against Strategic Traders
https://epubs.siam.org/doi/abs/10.1137/22M1486492?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1080-1112, December 2023. <br/> Abstract. We design a market-making model à la Avellaneda and Stoikov [Quant. Finance, 8 (2008), pp. 217–224] in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers’ behavior, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB-Fokker–Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviors for the market-takers and takes into account the impact of their strategies on the price process.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1080-1112, December 2023. <br/> Abstract. We design a market-making model à la Avellaneda and Stoikov [Quant. Finance, 8 (2008), pp. 217–224] in which the market-takers act strategically, in the sense that they design their trading strategy based on an exogenous trading signal. The market-maker chooses her quotes based on the average market-takers’ behavior, modelled through a mean-field interaction. We derive, up to the resolution of a coupled HJB-Fokker–Planck system, the optimal controls of the market-maker and the representative market-taker. This approach is flexible enough to incorporate different behaviors for the market-takers and takes into account the impact of their strategies on the price process.
A Mean-Field Game of Market-Making against Strategic Traders
10.1137/22M1486492
SIAM Journal on Financial Mathematics
2023-10-18T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Bastien Baldacci
Philippe Bergault
Dylan Possamaï
A Mean-Field Game of Market-Making against Strategic Traders
14
4
1080
1112
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1486492
https://epubs.siam.org/doi/abs/10.1137/22M1486492?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Pricing Bermudan Options Using Regression Trees/Random Forests
https://epubs.siam.org/doi/abs/10.1137/21M1460648?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1113-1139, December 2023. <br/> Abstract. The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In Longstaff and Schwartz [Rev. Financ. Studies, 14 (2001), pp. 113–147], these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using regression trees or random forests. We discuss the convergence of the Longstaff and Schwartz algorithm when the standard least squares regression is replaced by regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1113-1139, December 2023. <br/> Abstract. The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In Longstaff and Schwartz [Rev. Financ. Studies, 14 (2001), pp. 113–147], these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using regression trees or random forests. We discuss the convergence of the Longstaff and Schwartz algorithm when the standard least squares regression is replaced by regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.
Pricing Bermudan Options Using Regression Trees/Random Forests
10.1137/21M1460648
SIAM Journal on Financial Mathematics
2023-10-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Zineb El Filali Ech-Chafiq
Pierre Henry Labordère
Jérôme Lelong
Pricing Bermudan Options Using Regression Trees/Random Forests
14
4
1113
1139
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/21M1460648
https://epubs.siam.org/doi/abs/10.1137/21M1460648?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Relative Growth Rate Optimization Under Behavioral Criterion
https://epubs.siam.org/doi/abs/10.1137/22M1496943?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1140-1174, December 2023. <br/> Abstract. This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of [math]-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. Instead, we use the martingale method, concavification, and quantile optimization techniques to derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to S. Zhang, H. Q. Jin, and X. Zhou [Acta Math. Sin. (Engl. Ser.), 27 (2011), pp. 255–274] where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor’s risk tolerance level is high and the market state is bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1140-1174, December 2023. <br/> Abstract. This paper studies a continuous-time optimal portfolio selection problem in a complete market for a behavioral investor whose preference is of the prospect type with probability distortion. The investor is concerned with the terminal relative growth rate (log-return) instead of absolute capital value. This model can be regarded as an extension of the classical growth optimal problem to the behavioral framework. It leads to a new type of [math]-shaped utility maximization problem under nonlinear Choquet expectation. Due to the presence of probability distortion, the classical stochastic control methods are not applicable. Instead, we use the martingale method, concavification, and quantile optimization techniques to derive the closed-form optimal growth rate. We find that the benchmark growth rate has a significant impact on investment behaviors. Compared to S. Zhang, H. Q. Jin, and X. Zhou [Acta Math. Sin. (Engl. Ser.), 27 (2011), pp. 255–274] where the same preference measure is applied to the terminal relative wealth, we find a new phenomenon when the investor’s risk tolerance level is high and the market state is bad. In addition, our optimal wealth in every scenario is less sensitive to the pricing kernel and thus more stable than theirs.
Relative Growth Rate Optimization Under Behavioral Criterion
10.1137/22M1496943
SIAM Journal on Financial Mathematics
2023-10-25T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Jing Peng
Pengyu Wei
Zuo Quan Xu
Relative Growth Rate Optimization Under Behavioral Criterion
14
4
1140
1174
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1496943
https://epubs.siam.org/doi/abs/10.1137/22M1496943?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Portfolio Optimization within a Wasserstein Ball
https://epubs.siam.org/doi/abs/10.1137/22M1496803?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1175-1214, December 2023. <br/> Abstract. We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy’s risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lies within a Wasserstein ball surrounding a benchmark’s terminal wealth—being distributionally close—and that have a specified dependence/copula tying state-by-state outcomes to it. The investor then chooses the alternative strategy that minimizes a distortion risk measure of terminal wealth. In a general complete market model, we prove that an optimal dynamic strategy exists and provide its characterization through the notion of isotonic projections. We further propose a simulation approach to calculate the optimal strategy’s terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors’ optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark’s structure.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1175-1214, December 2023. <br/> Abstract. We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy’s risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lies within a Wasserstein ball surrounding a benchmark’s terminal wealth—being distributionally close—and that have a specified dependence/copula tying state-by-state outcomes to it. The investor then chooses the alternative strategy that minimizes a distortion risk measure of terminal wealth. In a general complete market model, we prove that an optimal dynamic strategy exists and provide its characterization through the notion of isotonic projections. We further propose a simulation approach to calculate the optimal strategy’s terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors’ optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark’s structure.
Portfolio Optimization within a Wasserstein Ball
10.1137/22M1496803
SIAM Journal on Financial Mathematics
2023-11-03T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Silvana M. Pesenti
Sebastian Jaimungal
Portfolio Optimization within a Wasserstein Ball
14
4
1175
1214
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1496803
https://epubs.siam.org/doi/abs/10.1137/22M1496803?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
On Bid and Ask Side-Specific Tick Sizes
https://epubs.siam.org/doi/abs/10.1137/21M146065X?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1215-1248, December 2023. <br/> Abstract. The tick size, which is the smallest increment between two consecutive prices for a given asset, is a key parameter of market microstructure. In particular, the behavior of high frequency market makers is highly related to its value. We take the point of view of an exchange and investigate the relevance of having different tick sizes on the bid and ask sides of the order-book. Using an approach based on the model with uncertainty zones, we show that when side-specific tick sizes are suitably chosen, it enables the exchange to improve the quality of liquidity provision.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1215-1248, December 2023. <br/> Abstract. The tick size, which is the smallest increment between two consecutive prices for a given asset, is a key parameter of market microstructure. In particular, the behavior of high frequency market makers is highly related to its value. We take the point of view of an exchange and investigate the relevance of having different tick sizes on the bid and ask sides of the order-book. Using an approach based on the model with uncertainty zones, we show that when side-specific tick sizes are suitably chosen, it enables the exchange to improve the quality of liquidity provision.
On Bid and Ask Side-Specific Tick Sizes
10.1137/21M146065X
SIAM Journal on Financial Mathematics
2023-11-09T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Bastien Baldacci
Philippe Bergault
Joffrey Derchu
Mathieu Rosenbaum
On Bid and Ask Side-Specific Tick Sizes
14
4
1215
1248
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/21M146065X
https://epubs.siam.org/doi/abs/10.1137/21M146065X?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning
https://epubs.siam.org/doi/abs/10.1137/22M1527209?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1249-1289, December 2023. <br/> Abstract.We propose a novel framework to solve risk-sensitive reinforcement learning problems where the agent optimizes time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our methodology constructs (strictly consistent) scoring functions that are used as penalizers in the estimation procedure. Our contribution is threefold: we (i) devise an efficient approach to estimate a class of dynamic spectral risk measures with deep neural networks, (ii) prove that these dynamic spectral risk measures may be approximated to any arbitrary accuracy using deep neural networks, and (iii) develop a risk-sensitive actor-critic algorithm that uses full episodes and does not require any additional nested transitions. We compare our conceptually improved reinforcement learning algorithm with the nested simulation approach and illustrate its performance in two settings: statistical arbitrage and portfolio allocation on both simulated and real data.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1249-1289, December 2023. <br/> Abstract.We propose a novel framework to solve risk-sensitive reinforcement learning problems where the agent optimizes time-consistent dynamic spectral risk measures. Based on the notion of conditional elicitability, our methodology constructs (strictly consistent) scoring functions that are used as penalizers in the estimation procedure. Our contribution is threefold: we (i) devise an efficient approach to estimate a class of dynamic spectral risk measures with deep neural networks, (ii) prove that these dynamic spectral risk measures may be approximated to any arbitrary accuracy using deep neural networks, and (iii) develop a risk-sensitive actor-critic algorithm that uses full episodes and does not require any additional nested transitions. We compare our conceptually improved reinforcement learning algorithm with the nested simulation approach and illustrate its performance in two settings: statistical arbitrage and portfolio allocation on both simulated and real data.
Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning
10.1137/22M1527209
SIAM Journal on Financial Mathematics
2023-11-14T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Anthony Coache
Sebastian Jaimungal
Álvaro Cartea
Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning
14
4
1249
1289
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1527209
https://epubs.siam.org/doi/abs/10.1137/22M1527209?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems
https://epubs.siam.org/doi/abs/10.1137/22M1539952?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1290-1303, December 2023. <br/> Abstract. The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [J. Han, A. Jentzen, and W. E, Proc. Natl. Acad. Sci. USA, 115 (2018), pp. 8505–8510] has shown great power in solving high-dimensional forward-backward stochastic differential equations and has inspired many applications. However, the method solves backward stochastic differential equations (BSDEs) in a forward manner, which cannot be used for optimal stopping problems that in general require running BSDE backwardly. To overcome this difficulty, a recent paper [H. Wang et al., Deep Learning-Based BSDE Solver for LIBOR Market Model with Application to Bermudan Swaption Pricing and Hedging, arXiv:1807.06622, 2018] proposed the backward deep BSDE method to solve the optimal stopping problem. In this paper, we provide a rigorous theory for the backward deep BSDE method. Specifically, (1) we derive the a posteriori error estimation, i.e., the error of the numerical solution can be bounded by the training loss function; and (2) we give an upper bound of the loss function, which can be sufficiently small subject to universal approximations. We give two numerical examples, which present consistent performance with the proved theory.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1290-1303, December 2023. <br/> Abstract. The optimal stopping problem is one of the core problems in financial markets, with broad applications such as pricing American and Bermudan options. The deep BSDE method [J. Han, A. Jentzen, and W. E, Proc. Natl. Acad. Sci. USA, 115 (2018), pp. 8505–8510] has shown great power in solving high-dimensional forward-backward stochastic differential equations and has inspired many applications. However, the method solves backward stochastic differential equations (BSDEs) in a forward manner, which cannot be used for optimal stopping problems that in general require running BSDE backwardly. To overcome this difficulty, a recent paper [H. Wang et al., Deep Learning-Based BSDE Solver for LIBOR Market Model with Application to Bermudan Swaption Pricing and Hedging, arXiv:1807.06622, 2018] proposed the backward deep BSDE method to solve the optimal stopping problem. In this paper, we provide a rigorous theory for the backward deep BSDE method. Specifically, (1) we derive the a posteriori error estimation, i.e., the error of the numerical solution can be bounded by the training loss function; and (2) we give an upper bound of the loss function, which can be sufficiently small subject to universal approximations. We give two numerical examples, which present consistent performance with the proved theory.
Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems
10.1137/22M1539952
SIAM Journal on Financial Mathematics
2023-12-04T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Chengfan Gao
Siping Gao
Ruimeng Hu
Zimu Zhu
Convergence of the Backward Deep BSDE Method with Applications to Optimal Stopping Problems
14
4
1290
1303
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1539952
https://epubs.siam.org/doi/abs/10.1137/22M1539952?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Liquidity Based Modeling of Asset Price Bubbles via Random Matching
https://epubs.siam.org/doi/abs/10.1137/22M1531580?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page 1304-1342, December 2023. <br/> Abstract. In this paper we study the evolution of asset price bubbles driven by contagion effects spreading among investors via a random matching mechanism in a discrete-time version of the liquidity based model of [R. A. Jarrow, P. Protter, and A. F. Roch, Quant. Finance, 12 (2012), pp. 1339–1349]. To this scope, we extend the Markov conditionally independent dynamic directed random matching of [D. Duffie, L. Qiao, and Y. Sun, J. Econ. Theory, 174 (2018), pp. 124–183] to a stochastic setting to include stochastic exogenous factors in the model. We derive conditions guaranteeing that the financial market model is arbitrage-free and present some numerical simulation illustrating our approach.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page 1304-1342, December 2023. <br/> Abstract. In this paper we study the evolution of asset price bubbles driven by contagion effects spreading among investors via a random matching mechanism in a discrete-time version of the liquidity based model of [R. A. Jarrow, P. Protter, and A. F. Roch, Quant. Finance, 12 (2012), pp. 1339–1349]. To this scope, we extend the Markov conditionally independent dynamic directed random matching of [D. Duffie, L. Qiao, and Y. Sun, J. Econ. Theory, 174 (2018), pp. 124–183] to a stochastic setting to include stochastic exogenous factors in the model. We derive conditions guaranteeing that the financial market model is arbitrage-free and present some numerical simulation illustrating our approach.
Liquidity Based Modeling of Asset Price Bubbles via Random Matching
10.1137/22M1531580
SIAM Journal on Financial Mathematics
2023-12-15T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Francesca Biagini
Andrea Mazzon
Thilo Meyer-Brandis
Katharina Oberpriller
Liquidity Based Modeling of Asset Price Bubbles via Random Matching
14
4
1304
1342
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/22M1531580
https://epubs.siam.org/doi/abs/10.1137/22M1531580?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Short Communication: Is a Sophisticated Agent Always a Wise One?
https://epubs.siam.org/doi/abs/10.1137/23M1569137?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page SC42-SC48, December 2023. <br/> Abstract. For time-inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by sophisticated agents. In this short note, we construct a deterministic continuous-time example where the unique equilibrium is dominated by another control. Therefore, in this situation, it may not be wise to take the equilibrium strategy.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC42-SC48, December 2023. <br/> Abstract. For time-inconsistent optimal control problems, a quite popular approach is the equilibrium approach, taken by sophisticated agents. In this short note, we construct a deterministic continuous-time example where the unique equilibrium is dominated by another control. Therefore, in this situation, it may not be wise to take the equilibrium strategy.
Short Communication: Is a Sophisticated Agent Always a Wise One?
10.1137/23M1569137
SIAM Journal on Financial Mathematics
2023-10-17T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Jianfeng Zhang
Short Communication: Is a Sophisticated Agent Always a Wise One?
14
4
SC42
SC48
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/23M1569137
https://epubs.siam.org/doi/abs/10.1137/23M1569137?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Short Communication: The Birth of (a Robust) Arbitrage Theory in de Finetti’s Early Contributions
https://epubs.siam.org/doi/abs/10.1137/23M1604096?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page SC49-SC59, December 2023. <br/> Abstract. Il significato soggettivo della probabilità (1931) by B. de Finetti is unanimously considered the rise of “subjectivism,” a notion which strongly influenced both probability and decision theory. What is less acknowledged is that in 1931 de Finetti posed the foundations of modern arbitrage theory. In this paper we aim at examining how de Finetti’s contribution should be considered as the precursor of asset pricing theory and we show how his findings relate to recent developments in robust finance.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC49-SC59, December 2023. <br/> Abstract. Il significato soggettivo della probabilità (1931) by B. de Finetti is unanimously considered the rise of “subjectivism,” a notion which strongly influenced both probability and decision theory. What is less acknowledged is that in 1931 de Finetti posed the foundations of modern arbitrage theory. In this paper we aim at examining how de Finetti’s contribution should be considered as the precursor of asset pricing theory and we show how his findings relate to recent developments in robust finance.
Short Communication: The Birth of (a Robust) Arbitrage Theory in de Finetti’s Early Contributions
10.1137/23M1604096
SIAM Journal on Financial Mathematics
2023-11-15T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Marco Maggis
Short Communication: The Birth of (a Robust) Arbitrage Theory in de Finetti’s Early Contributions
14
4
SC49
SC59
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/23M1604096
https://epubs.siam.org/doi/abs/10.1137/23M1604096?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics
-
Short Communication: Existence of Markov Equilibrium Control in Discrete Time
https://epubs.siam.org/doi/abs/10.1137/23M1594121?ai=s8&mi=3f5qtr&af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/14/4">Volume 14, Issue 4</a>, Page SC60-SC71, December 2023. <br/> Abstract. For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Björk and Murgoci [Finance Stoch., 18 (2014), pp. 545–592] is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium policy exists if the objective is inf-compact in every time step. We provide a sufficient condition for the inf-compactness and thus existence with costs that are lower semicontinuous and bounded from below and transition kernels that are continuous in controls under given states. The control spaces need not to be compact.
SIAM Journal on Financial Mathematics, Volume 14, Issue 4, Page SC60-SC71, December 2023. <br/> Abstract. For time-inconsistent stochastic controls in discrete time and finite horizon, an open problem in Björk and Murgoci [Finance Stoch., 18 (2014), pp. 545–592] is the existence of an equilibrium control. A nonrandomized Borel measurable Markov equilibrium policy exists if the objective is inf-compact in every time step. We provide a sufficient condition for the inf-compactness and thus existence with costs that are lower semicontinuous and bounded from below and transition kernels that are continuous in controls under given states. The control spaces need not to be compact.
Short Communication: Existence of Markov Equilibrium Control in Discrete Time
10.1137/23M1594121
SIAM Journal on Financial Mathematics
2023-12-08T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Erhan Bayraktar
Bingyan Han
Short Communication: Existence of Markov Equilibrium Control in Discrete Time
14
4
SC60
SC71
2023-12-31T08:00:00Z
2023-12-31T08:00:00Z
10.1137/23M1594121
https://epubs.siam.org/doi/abs/10.1137/23M1594121?ai=s8&mi=3f5qtr&af=R
© 2023 Society for Industrial and Applied Mathematics