Robust Utility Maximizing Strategies under Model Uncertainty and their Convergence

TL;DR

This paper develops explicit robust utility maximization strategies in incomplete markets with drift uncertainty, proving their convergence to diversification as uncertainty grows, and establishes a minimax duality result.

Contribution

It provides explicit solutions for robust strategies under ellipsoidal drift uncertainty and proves their convergence and a minimax duality theorem.

Findings

Explicit optimal strategies derived under drift uncertainty.

Convergence of strategies to uniform diversification with increasing uncertainty.

Establishment of a minimax duality theorem.

Abstract

In this paper we investigate a utility maximization problem with drift uncertainty in a multivariate continuous-time Black-Scholes type financial market which may be incomplete. We impose a constraint on the admissible strategies that prevents a pure bond investment and we include uncertainty by means of ellipsoidal uncertainty sets for the drift. Our main results consist firstly in finding an explicit representation of the optimal strategy and the worst-case parameter, secondly in proving a minimax theorem that connects our robust utility maximization problem with the corresponding dual problem. Thirdly, we show that, as the degree of model uncertainty increases, the optimal strategy converges to a generalized uniform diversification strategy.