English

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

Optimization and Control 2024-01-17 v2 Probability Mathematical Finance

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 P\mathbb{P} with an adverse choice from a Wasserstein ball of radius kk around P\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 kk tends to infinity.

Keywords

Cite

@article{arxiv.2306.01503,
  title  = {Strategies with minimal norm are optimal for expected utility maximization under high model ambiguity},
  author = {Laurence Carassus and Johannes Wiesel},
  journal= {arXiv preprint arXiv:2306.01503},
  year   = {2024}
}

Comments

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