标题： 具有最小范数的策略在高模型不确定性下对于期望效用最大化是最佳的 显示英文标题

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

摘要： 我们研究了一个在单期金融市场中存在模型不确定性的期望效用最大化问题。 我们通过将基准模型$\mathbb{P}$替换为概率测度空间中以$\mathbb{P}$为中心、半径为$k$的Wasserstein球中的不利选择来捕捉模型不确定性，并考虑相应的Wasserstein分布鲁棒优化问题。 我们证明了当不确定性越来越大时，即当半径$k$趋向于无穷大时，最优解收敛到一个具有最小范数的策略。 显示英文摘要

摘要： 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.