Optimal Growth under Model Uncertainty
23 Pages Posted: 8 Oct 2020 Last revised: 16 Feb 2021
Date Written: August 20, 2020
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: Suggested Citation