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

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 ℙ with an adverse choice from a Wasserstein ball of radius k around 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.