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?af=R
Society for Industrial and Applied Mathematics: SIAM Journal on Financial Mathematics: Table of Contents
Society for Industrial and Applied Mathematics
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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?af=R

On Robust Fundamental Theorems of Asset Pricing in Discrete Time
https://epubs.siam.org/doi/abs/10.1137/23M156032X?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 571600, September 2024. <br/> Abstract.This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modeled by a (possibly uncountable) family of price processes on the same probability space. Our technical assumption is the continuity of the price processes with respect to uncertain parameters. In this setting, we introduce a new topological framework which allows us to use the classical arguments in arbitrage pricing theory involving Lp spaces, the Hahn–Banach separation theorem, and other tools from functional analysis. The first result is the equivalence of a “no robust arbitrage” condition and the existence of a new “robust pricing system.” The second result shows superhedging dualities and the existence of superhedging strategies without restrictive conditions on payoff functions, in contrast to other related studies. The third result discusses completeness in the present robust setting. When other options are available for static trading, we could reduce the set of robust pricing systems and hence the superhedging prices.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 571600, September 2024. <br/> Abstract.This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modeled by a (possibly uncountable) family of price processes on the same probability space. Our technical assumption is the continuity of the price processes with respect to uncertain parameters. In this setting, we introduce a new topological framework which allows us to use the classical arguments in arbitrage pricing theory involving Lp spaces, the Hahn–Banach separation theorem, and other tools from functional analysis. The first result is the equivalence of a “no robust arbitrage” condition and the existence of a new “robust pricing system.” The second result shows superhedging dualities and the existence of superhedging strategies without restrictive conditions on payoff functions, in contrast to other related studies. The third result discusses completeness in the present robust setting. When other options are available for static trading, we could reduce the set of robust pricing systems and hence the superhedging prices. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
On Robust Fundamental Theorems of Asset Pricing in Discrete Time
10.1137/23M156032X
SIAM Journal on Financial Mathematics
20240704T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Huy N. Chau
On Robust Fundamental Theorems of Asset Pricing in Discrete Time
15
3
571
600
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M156032X
https://epubs.siam.org/doi/abs/10.1137/23M156032X?af=R
© 2024 Society for Industrial and Applied Mathematics

Partial Hedging in Rough Volatility Models
https://epubs.siam.org/doi/abs/10.1137/23M1583090?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 601652, September 2024. <br/> Abstract.This paper studies the problem of partial hedging within the framework of rough volatility models in an incomplete market setting. We employ a stochastic control problem formulation to minimize the discrepancy between a stochastic target and the terminal value of a hedging portfolio. As rough volatility models are neither Markovian nor semimartingales, stochastic control problems associated with rough models are quite complex to solve. Therefore, we propose a multifactor approximation of the rough volatility model and introduce the associated Markov stochastic control problem. We establish the convergence of the optimal solution for the Markov partial hedging problem to the optimal solution of the original problem as the number of factors tends to infinity. Furthermore, the optimal solution of the Markov problem can be derived by solving a Hamilton–Jacobi–Bellman equation and more precisely a nonlinear partial differential equation (PDE). Due to the inherent complexity of this nonlinear PDE, an explicit formula for the optimal solution is generally unattainable. By introducing the dual solution of the Markov problem and expressing the primal solution as a function of the dual solution, we derive approximate solutions to the Markov problem using a dual control method. This method allows for suboptimal choices of dual control to deduce lower and upper bounds on the optimal solution as well as suboptimal hedging ratios. In particular, explicit formulas for partial hedging strategies in a rough Heston model are derived.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 601652, September 2024. <br/> Abstract.This paper studies the problem of partial hedging within the framework of rough volatility models in an incomplete market setting. We employ a stochastic control problem formulation to minimize the discrepancy between a stochastic target and the terminal value of a hedging portfolio. As rough volatility models are neither Markovian nor semimartingales, stochastic control problems associated with rough models are quite complex to solve. Therefore, we propose a multifactor approximation of the rough volatility model and introduce the associated Markov stochastic control problem. We establish the convergence of the optimal solution for the Markov partial hedging problem to the optimal solution of the original problem as the number of factors tends to infinity. Furthermore, the optimal solution of the Markov problem can be derived by solving a Hamilton–Jacobi–Bellman equation and more precisely a nonlinear partial differential equation (PDE). Due to the inherent complexity of this nonlinear PDE, an explicit formula for the optimal solution is generally unattainable. By introducing the dual solution of the Markov problem and expressing the primal solution as a function of the dual solution, we derive approximate solutions to the Markov problem using a dual control method. This method allows for suboptimal choices of dual control to deduce lower and upper bounds on the optimal solution as well as suboptimal hedging ratios. In particular, explicit formulas for partial hedging strategies in a rough Heston model are derived. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Partial Hedging in Rough Volatility Models
10.1137/23M1583090
SIAM Journal on Financial Mathematics
20240705T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Edouard Motte
Donatien Hainaut
Partial Hedging in Rough Volatility Models
15
3
601
652
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1583090
https://epubs.siam.org/doi/abs/10.1137/23M1583090?af=R
© 2024 Society for Industrial and Applied Mathematics

Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost
https://epubs.siam.org/doi/abs/10.1137/23M1571058?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 653699, September 2024. <br/> Abstract.A novel highfrequency market making approach in discrete time is proposed that admits closedform solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand’s randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the nonadaptive strategy and those that quote limit orders at a fixed distance from the midprice.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 653699, September 2024. <br/> Abstract.A novel highfrequency market making approach in discrete time is proposed that admits closedform solutions. By taking advantage of demand functions that are linear in the quoted bid and ask spreads with random coefficients, we model the variability of the partial filling of limit orders posted in a limit order book (LOB). As a result, we uncover new patterns as to how the demand’s randomness affects the optimal placement strategy. We also allow the price process to follow general dynamics without any Brownian or martingale assumption as is commonly adopted in the literature. The most important feature of our optimal placement strategy is that it can react or adapt to the behavior of market orders online. Using LOB data, we train our model and reproduce the anticipated final profit and loss of the optimal strategy on a given testing date using the actual flow of orders in the LOB. Our adaptive optimal strategies outperform the nonadaptive strategy and those that quote limit orders at a fixed distance from the midprice. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost
10.1137/23M1571058
SIAM Journal on Financial Mathematics
20240731T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jonathan ChávezCasillas
José E. FigueroaLópez
Chuyi Yu
Yi Zhang
Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost
15
3
653
699
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1571058
https://epubs.siam.org/doi/abs/10.1137/23M1571058?af=R
© 2024 Society for Industrial and Applied Mathematics

Estimation of Systemic Shortfall Risk Measure Using Stochastic Algorithms
https://epubs.siam.org/doi/abs/10.1137/22M1539344?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 700733, September 2024. <br/> Abstract.Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that are generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating multivariate shortfall risk measure and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 700733, September 2024. <br/> Abstract.Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that are generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating multivariate shortfall risk measure and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Estimation of Systemic Shortfall Risk Measure Using Stochastic Algorithms
10.1137/22M1539344
SIAM Journal on Financial Mathematics
20240808T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Sarah Kaakaï
Anis Matoussi
Achraf Tamtalini
Estimation of Systemic Shortfall Risk Measure Using Stochastic Algorithms
15
3
700
733
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/22M1539344
https://epubs.siam.org/doi/abs/10.1137/22M1539344?af=R
© 2024 Society for Industrial and Applied Mathematics

Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models
https://epubs.siam.org/doi/abs/10.1137/23M1606769?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 734784, September 2024. <br/> Abstract.We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a [math]dimensional risky asset as functions of the underlying model parameters, payoff parameters, and initial conditions. We cover a general class of stochastic volatility models of Markovian nature as well as the rough Bergomi model. In particular, under suitable assumptions we show that option prices can be learned by DNNs up to an arbitrary small error [math] while the network size grows only subpolynomially in the asset vector dimension [math] and the reciprocal [math] of the accuracy. Hence, the approximation does not suffer from the curse of dimensionality. As quantitative approximation results for DNNs applicable in our setting are formulated for functions on compact domains, we first consider the case of the asset price restricted to a compact set, and then we extend these results to the general case by using convergence arguments for the option prices.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 734784, September 2024. <br/> Abstract.We derive quantitative error bounds for deep neural networks (DNNs) approximating option prices on a [math]dimensional risky asset as functions of the underlying model parameters, payoff parameters, and initial conditions. We cover a general class of stochastic volatility models of Markovian nature as well as the rough Bergomi model. In particular, under suitable assumptions we show that option prices can be learned by DNNs up to an arbitrary small error [math] while the network size grows only subpolynomially in the asset vector dimension [math] and the reciprocal [math] of the accuracy. Hence, the approximation does not suffer from the curse of dimensionality. As quantitative approximation results for DNNs applicable in our setting are formulated for functions on compact domains, we first consider the case of the asset price restricted to a compact set, and then we extend these results to the general case by using convergence arguments for the option prices. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models
10.1137/23M1606769
SIAM Journal on Financial Mathematics
20240819T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Francesca Biagini
Lukas Gonon
Niklas Walter
Approximation Rates for Deep Calibration of (Rough) Stochastic Volatility Models
15
3
734
784
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1606769
https://epubs.siam.org/doi/abs/10.1137/23M1606769?af=R
© 2024 Society for Industrial and Applied Mathematics

Reconciling Rough Volatility with Jumps
https://epubs.siam.org/doi/abs/10.1137/23M1558847?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 785823, September 2024. <br/> Abstract.We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large volofvols. Starting from hyperrough Heston models with a Hurst index [math], we derive a Markovian approximating class of onedimensional reversionary Hestontype models. Such proxies encode a tradeoff between an exploding volofvol and a fast meanreversion speed controlled by a reversionary timescale [math] and an unconstrained parameter [math]. Sending [math] to 0 yields convergence of the reversionary Heston model toward different explicit asymptotic regimes based on the value of the parameter [math]. In particular, for [math], the reversionary Heston model converges to a class of Lévy jump processes of normal inverse Gaussian type. Numerical illustrations show that the reversionary Heston model is capable of generating atthemoney skews similar to the ones generated by rough, hyperrough, and jump models.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 785823, September 2024. <br/> Abstract.We reconcile rough volatility models and jump models using a class of reversionary Heston models with fast mean reversions and large volofvols. Starting from hyperrough Heston models with a Hurst index [math], we derive a Markovian approximating class of onedimensional reversionary Hestontype models. Such proxies encode a tradeoff between an exploding volofvol and a fast meanreversion speed controlled by a reversionary timescale [math] and an unconstrained parameter [math]. Sending [math] to 0 yields convergence of the reversionary Heston model toward different explicit asymptotic regimes based on the value of the parameter [math]. In particular, for [math], the reversionary Heston model converges to a class of Lévy jump processes of normal inverse Gaussian type. Numerical illustrations show that the reversionary Heston model is capable of generating atthemoney skews similar to the ones generated by rough, hyperrough, and jump models. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Reconciling Rough Volatility with Jumps
10.1137/23M1558847
SIAM Journal on Financial Mathematics
20240906T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Eduardo Abi Jaber
Nathan De Carvalho
Reconciling Rough Volatility with Jumps
15
3
785
823
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1558847
https://epubs.siam.org/doi/abs/10.1137/23M1558847?af=R
© 2024 Society for Industrial and Applied Mathematics

Option Pricing in Sandwiched Volterra Volatility Model
https://epubs.siam.org/doi/abs/10.1137/22M1521328?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 824882, September 2024. <br/> Abstract.We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation, which ensures that the solution is “sandwiched” between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities, and study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 824882, September 2024. <br/> Abstract.We introduce a new model of financial market with stochastic volatility driven by an arbitrary Hölder continuous Gaussian Volterra process. The distinguishing feature of the model is the form of the volatility equation, which ensures that the solution is “sandwiched” between two arbitrary Hölder continuous functions chosen in advance. We discuss the structure of local martingale measures on this market, investigate integrability and Malliavin differentiability of prices and volatilities, and study absolute continuity of the corresponding probability laws. Additionally, we utilize Malliavin calculus to develop an algorithm of pricing options with discontinuous payoffs. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Option Pricing in Sandwiched Volterra Volatility Model
10.1137/22M1521328
SIAM Journal on Financial Mathematics
20240909T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Giulia Di Nunno
Yuliya Mishura
Anton YurchenkoTytarenko
Option Pricing in Sandwiched Volterra Volatility Model
15
3
824
882
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/22M1521328
https://epubs.siam.org/doi/abs/10.1137/22M1521328?af=R
© 2024 Society for Industrial and Applied Mathematics

A TwoPerson ZeroSum Game Approach for a Retirement Decision with Borrowing Constraints
https://epubs.siam.org/doi/abs/10.1137/22M1528124?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 883930, September 2024. <br/> Abstract. We study an optimal consumption, investment, and retirement decision of an economic agent with borrowing constraints under a general class of utility functions. We transform the problem into a dual twoperson zerosum game, which involves two players: a stopper who is a maximizer and chooses a stopping time and a controller who is a minimizer and chooses a nonincreasing process. We derive the Hamilton–Jacobi–Bellman quasivariational inequality (HJBQVI) of a maxmin type from the dual twoperson zerosum game. We provide a solution to the HJBQVI and verify that the solution to the HJBQVI is the value of the dual twoperson zerosum game. We establish the duality result which allows us to derive the optimal strategies and value function of the primal problem from those of the dual problem. We provide examples for a class of utility functions.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 883930, September 2024. <br/> Abstract. We study an optimal consumption, investment, and retirement decision of an economic agent with borrowing constraints under a general class of utility functions. We transform the problem into a dual twoperson zerosum game, which involves two players: a stopper who is a maximizer and chooses a stopping time and a controller who is a minimizer and chooses a nonincreasing process. We derive the Hamilton–Jacobi–Bellman quasivariational inequality (HJBQVI) of a maxmin type from the dual twoperson zerosum game. We provide a solution to the HJBQVI and verify that the solution to the HJBQVI is the value of the dual twoperson zerosum game. We establish the duality result which allows us to derive the optimal strategies and value function of the primal problem from those of the dual problem. We provide examples for a class of utility functions. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
A TwoPerson ZeroSum Game Approach for a Retirement Decision with Borrowing Constraints
10.1137/22M1528124
SIAM Journal on Financial Mathematics
20240911T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Junkee Jeon
Hyeng Keun Koo
Minsuk Kwak
A TwoPerson ZeroSum Game Approach for a Retirement Decision with Borrowing Constraints
15
3
883
930
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/22M1528124
https://epubs.siam.org/doi/abs/10.1137/22M1528124?af=R
© 2024 Society for Industrial and Applied Mathematics

Decentralized Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision
https://epubs.siam.org/doi/abs/10.1137/23M1602103?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 931959, September 2024. <br/> Abstract. Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterize the continuoustime wealth dynamics of strategic liquidity providers (LPs) who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a selffinancing and closedform optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable loss (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the outofsample performance of our strategy is superior to the historical performance of LPs in the pool we consider.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 931959, September 2024. <br/> Abstract. Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterize the continuoustime wealth dynamics of strategic liquidity providers (LPs) who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a selffinancing and closedform optimal liquidity provision strategy where the width of the LP’s liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable loss (PL) of the LP’s position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP’s range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the outofsample performance of our strategy is superior to the historical performance of LPs in the pool we consider. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Decentralized Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision
10.1137/23M1602103
SIAM Journal on Financial Mathematics
20240917T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Álvaro Cartea
Fayçal Drissi
Marcello Monga
Decentralized Finance and Automated Market Making: Predictable Loss and Optimal Liquidity Provision
15
3
931
959
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1602103
https://epubs.siam.org/doi/abs/10.1137/23M1602103?af=R
© 2024 Society for Industrial and Applied Mathematics

A Mean Field Game Approach to Bitcoin Mining
https://epubs.siam.org/doi/abs/10.1137/23M1617813?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page 960987, September 2024. <br/> Abstract.We present an analysis of the ProofofWork consensus algorithm, used on the Bitcoin blockchain, using a mean field game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). This class of models allows us to adapt to many different situations. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress only. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain and the energy consumption either are constant or increase with the price of the underlying cryptocurrency.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 960987, September 2024. <br/> Abstract.We present an analysis of the ProofofWork consensus algorithm, used on the Bitcoin blockchain, using a mean field game framework. Using a master equation, we provide an equilibrium characterization of the total computational power devoted to mining the blockchain (hashrate). This class of models allows us to adapt to many different situations. The essential structure of the game is preserved across all the enrichments. In deterministic settings, the hashrate ultimately reaches a steady state in which it increases at the rate of technological progress only. In stochastic settings, there exists a target for the hashrate for every possible random state. As a consequence, we show that in equilibrium the security of the underlying blockchain and the energy consumption either are constant or increase with the price of the underlying cryptocurrency. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
A Mean Field Game Approach to Bitcoin Mining
10.1137/23M1617813
SIAM Journal on Financial Mathematics
20240918T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Charles Bertucci
Louis Bertucci
JeanMichel Lasry
PierreLouis Lions
A Mean Field Game Approach to Bitcoin Mining
15
3
960
987
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/23M1617813
https://epubs.siam.org/doi/abs/10.1137/23M1617813?af=R
© 2024 Society for Industrial and Applied Mathematics

Short Communication: The Price of Information
https://epubs.siam.org/doi/abs/10.1137/24M1644791?af=R
SIAM Journal on Financial Mathematics, <a href="https://epubs.siam.org/toc/sjfmbj/15/3">Volume 15, Issue 3</a>, Page SC54SC67, September 2024. <br/> Abstract.When an investor is faced with the option to purchase additional information regarding an asset price, how much should she pay? To address this question, we solve for the indifference price of information in a setting where a trader maximizes her expected utility of terminal wealth over a finite time horizon. If she does not purchase the information, then she solves a partial information stochastic control problem, while if she does purchase the information, then she pays a cost and receives partial information about the asset’s trajectory. We further demonstrate that when the investor can purchase the information at any stopping time prior to the end of the trading horizon, she chooses to do so at a deterministic time.
SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page SC54SC67, September 2024. <br/> Abstract.When an investor is faced with the option to purchase additional information regarding an asset price, how much should she pay? To address this question, we solve for the indifference price of information in a setting where a trader maximizes her expected utility of terminal wealth over a finite time horizon. If she does not purchase the information, then she solves a partial information stochastic control problem, while if she does purchase the information, then she pays a cost and receives partial information about the asset’s trajectory. We further demonstrate that when the investor can purchase the information at any stopping time prior to the end of the trading horizon, she chooses to do so at a deterministic time. <p><img src="https://epubs.siam.org/na101/home/literatum/publisher/siam/journals/covergifs/sjfmbj/cover.jpg" alttext="cover image"/></p>
Short Communication: The Price of Information
10.1137/24M1644791
SIAM Journal on Financial Mathematics
20240805T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Sebastian Jaimungal
Xiaofei Shi
Short Communication: The Price of Information
15
3
SC54
SC67
20240930T07:00:00Z
20240930T07:00:00Z
10.1137/24M1644791
https://epubs.siam.org/doi/abs/10.1137/24M1644791?af=R
© 2024 Society for Industrial and Applied Mathematics