Strategies with minimal norm are optimal for expected utility maximisation under high model ambiguity
研究单期金融市场中模型不确定下的期望效用最大化问题，用Wasserstein球刻画模型模糊性，发现当不确定性很大时，最优策略收敛到最小范数策略。
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.