Asymptotic Optimal Portfolio in Fast Mean-reverting Stochastic Environments

Ruimeng Hu

Papers from arXiv.org

Abstract: This paper studies the portfolio optimization problem when the investor's utility is general and the return and volatility of the risky asset are fast mean-reverting, which are important to capture the fast-time scale in the modeling of stock price volatility. Motivated by the heuristic derivation in [J.-P. Fouque, R. Sircar and T. Zariphopoulou, \emph{Mathematical Finance}, 2016], we propose a zeroth order strategy, and show its asymptotic optimality within a specific (smaller) family of admissible strategies under proper assumptions. This optimality result is achieved by establishing a first order approximation of the problem value associated to this proposed strategy using singular perturbation method, and estimating the risk-tolerance functions. The results are natural extensions of our previous work on portfolio optimization in a slowly varying stochastic environment [J.-P. Fouque and R. Hu, \emph{SIAM Journal on Control and Optimization}, 2017], and together they form a whole picture of analyzing portfolio optimization in both fast and slow environments.

Date: 2018-03, Revised 2019-01
New Economics Papers: this item is included in nep-upt
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1803.07720

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