Portfolio Optimization with Nondominated Priors and Unbounded Parameters

TL;DR

This paper addresses the complex problem of optimizing investment portfolios when both the mean and volatility of stock returns are unbounded and uncertain, using a novel approach to utility maximization under Knightian uncertainty.

Contribution

It introduces the first explicit solution to utility maximization with unbounded mean and volatility under nondominated priors and Knightian uncertainty.

Findings

Explicit solution to the utility maximization problem.

Handles unbounded mean and volatility.

Addresses Knightian uncertainty in portfolio optimization.

Abstract

We consider classical Merton problem of terminal wealth maximization in finite horizon. We assume that the drift of the stock is following Ornstein-Uhlenbeck process and the volatility of it is following GARCH(1) process. In particular, both mean and volatility are unbounded. We assume that there is Knightian uncertainty on the parameters of both mean and volatility. We take that the investor has logarithmic utility function, and solve the corresponding utility maximization problem explicitly. To the best of our knowledge, this is the first work on utility maximization with unbounded mean and volatility in Knightian uncertainty under nondominated priors.