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

Paper: arXiv 2306.01503

Authors: Laurence Carassus, Johannes Wiesel

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 $\mathbb{P}$ 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical analysis of expected utility maximization under Wasserstein distributionally robust optimization, offering strong mathematical proofs regarding minimal norm strategies under extreme ambiguity. However, it is entirely theoretical with minimal to no empirical validation or backtesting on real market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Utility Maximization under High Model Uncertainty] --> B[Inputs: Baseline Model P & Wasserstein Ball Radius k]
    B --> C[Methodology: Wasserstein Distributionally Robust Optimization]
    C --> D[Computational Process: Increase Ambiguity Radius k to Infinity]
    D --> E[Key Finding: Optimal Strategies Converge to Minimal Norm Solution]