@article{b6cc3700d603403fbecbff0a82911aec,
title = "Sub- and Supersolution Approach to Accuracy Analysis of Portfolio Optimization Asymptotics in Multiscale Stochastic Factor Markets",
abstract = "The problem of portfolio optimization when stochastic factors drive returns and volatilities has been studied in previous works by the authors. In particular, they proposed asymptotic approximations for value functions and optimal strategies in the regime where these factors are running on both slow and fast timescales. However, the rigorous justification of the accuracy of these approximations has been limited to power utilities and a single factor. In this paper, we provide an accurate analysis for cases with general utility functions and two timescale factors by constructing sub- and supersolutions to the fully nonlinear problem so that their difference is at the desired level of accuracy. This approach will be valuable in various related stochastic control problems.",
keywords = "portfolio optimization, rigorous asymptotics, stochastic volatility, subsolution, supersolution, utility maximization",
author = "Fouque, {Jean Pierre} and Ruimeng Hu and Ronnie Sircar",
note = "Funding Information: \ast Received by the editors June 22, 2021; accepted for publication (in revised form) October 15, 2021; published electronically January 31, 2022. https://doi.org/10.1137/21M1428625 Funding: The first author was supported by NSF grant DMS-1814091. The second author was partially supported by the NSF grant DMS-1953035, the Faculty Career Development Award, the Research Assistance Program Award, and the Early Career Faculty Acceleration funding at UCSB. \dagger Department of Statistics and Applied Probability, University of California Santa Barbara, Santa Barbara, CA 93106-3110 USA (jpfouque54@gmail.com). \ddagger Department of Mathematics, Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA 93111 USA (rhu@ucsb.edu). \S Operations Research \& Financial Engineering (ORFE) Department, Princeton University, Princeton, NJ 08544 USA (sircar@princeton.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2022",
doi = "10.1137/21M1428625",
language = "English (US)",
volume = "13",
pages = "109--128",
journal = "SIAM Journal on Financial Mathematics",
issn = "1945-497X",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}