Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity

Abstract

We investigate an expected utility maximization problem under model uncertainty in a one-period financial market. We capture model uncertainty by replacing the baseline model $\mathbb{P}$ with an adverse choice from a Wasserstein ball of radius $k$ around $\mathbb{P}$ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimization problem. We show that optimal solutions converge to a strategy with minimal norm when uncertainty is increasingly large, i.e. when the radius $k$ tends to infinity.

We have substantially generalized our main result, Theorem 1.1. We now consider general closed constraint sets $D$ and show that the optimal strategies converge to the one with minimal norm. In the case $D=\{w:<w,1>\ge a\}$ for some $a>0$ we recover the re-weighted uniform strategy