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

Abstract We investigate an expected utility maximisation 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 $k$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> around ℙ in the space of probability measures and consider the corresponding Wasserstein distributionally robust optimisation problem. We show that solutions converge to a strategy with minimal norm when uncertainty becomes large, i.e., when the radius $k$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>k</mml:mi> </mml:math> tends to infinity.