Functional Portfolio Optimization in Stochastic Portfolio Theory
Abstract
In this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave function on the unit interval. This choice can be motivated by the long term stability of the capital distribution observed in large equity markets and allows us to circumvent the curse of dimensionality. The resulting optimization problem, which is convex, allows for various regularizations and constraints to be imposed on the generating function. We prove an existence and uniqueness result for our optimization problem and provide a stability estimate in terms of a Wasserstein metric of the input measure. Then we formulate a discretization which can be implemented numerically using available software packages and analyze its approximation error. Finally, we present empirical examples using CRSP data from the U.S. stock market, including the performance of the portfolios allowing for dividends, defaults, and transaction costs.
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Information & Authors
Information
Published In
SIAM Journal on Financial Mathematics
Pages: 576 - 618
DOI: 10.1137/21M1417715
ISSN (online): 1945-497X
Copyright
© 2022, Society for Industrial and Applied Mathematics.
History
Submitted: 5 May 2021
Accepted: 23 January 2022
Published online: 5 May 2022
Keywords
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Authors
Funding Information
Natural Sciences and Engineering Research Council of Canada https://doi.org/10.13039/501100000038 : RGPIN-2019-04419, CGSD3-535625-2019
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