Robust Portfolio Selection under State-dependent Confidence Set

TL;DR

This paper develops a robust portfolio optimization model considering state-dependent confidence sets for drift uncertainty, incorporating Bayesian learning, and derives a semi-analytical investment strategy with practical implications.

Contribution

It introduces a novel approach to robust portfolio selection with state-dependent confidence sets and Bayesian learning, providing explicit strategies and PDE analysis.

Findings

Robust strategy includes myopic and hedging components.

Optimal strategy varies across buying, selling, and small trading regions.

Learning reduces uncertainty, increasing risk exposure over time.

Abstract

This paper studies the robust portfolio selection problem under a state-dependent confidence set. The investor invests in a financial market with a risk-free asset and a risky asset. The ambiguity-averse investor faces uncertainty over the drift of the risky asset and updates posterior beliefs by Bayesian learning. The investor holds the belief that the unknown drift falls within a confidence set at a certain confidence level. The confidence set varies with both the observed state and time. By maximizing the expected CARA utility of terminal wealth under the worst-case scenario of the unknown drift, we derive and solve the associated HJBI equation. The robust optimal investment strategy is obtained in a semi-analytical form based on a PDE. We validate the existence and uniqueness of the PDE and demonstrate the optimality of the solution in the verification theorem. The robust optimal investment strategy consists of two components: myopic demand in the worst-case scenario and hedging demand. The robust optimal investment strategy is categorized into three regions: buying, selling, and small trading. Ambiguity aversion results in a more conservative robust optimal investment strategy. Additionally, with learning, the investor's uncertainty about the drift decreases over time, leading to increased risk exposure to the risky asset.