Optimal Growth under Model Uncertainty

23 Pages Posted: 8 Oct 2020 Last revised: 16 Feb 2021

Date Written: August 20, 2020

Abstract

The optimal growth of a wealth process toward a goal is studied under ambiguous markets with first- and second-order moment uncertainties relating to stock returns. Optimal strategies and value functions are solved explicitly. A verification theorem is proved to show that the results solve the original stochastic control problem. Quantitative analyses of the investment strategies indicate that a rational individual with ambiguity aversion reduces market participation when return and volatility are uncorrelated, while there is an exception for synchronous return and volatility. The welfare of shorting a discounted reward is computed, which demonstrates that in an ambiguous pricing economy, investors can generate a positive premium via appropriate asset allocations.

Keywords: Optimal Growth; Asset Allocation; Kelly Criterion; Model Uncertainty

JEL Classification: C61; D81; G11

Suggested Citation

Xu, Yuhong, Optimal Growth under Model Uncertainty (August 20, 2020). Available at SSRN: https://ssrn.com/abstract=3677659 or http://dx.doi.org/10.2139/ssrn.3677659

Yuhong Xu (Contact Author)

Soochow university ( email )

No. 1 Shizi Street
Suzhou, Jiangsu 215006
China

HOME PAGE: http://web.suda.edu.cn/yhxu/

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