Optimal payoff under Bregman-Wasserstein divergence constraints

ArXiv ID: 2411.18397 “View on arXiv”

Authors: Unknown

Abstract

We study optimal payoff choice for an expected utility maximizer under the constraint that their payoff is not allowed to deviate ``too much’’ from a given benchmark. We solve this problem when the deviation is assessed via a Bregman-Wasserstein (BW) divergence, generated by a convex function $φ$. Unlike the Wasserstein distance (i.e., when $φ(x)=x^2$) the inherent asymmetry of the BW divergence makes it possible to penalize positive deviations different than negative ones. As a main contribution, we provide the optimal payoff in this setting. Numerical examples illustrate that the choice of $φ$ allow to better align the payoff choice with the objectives of investors.

Keywords: Bregman-Wasserstein Divergence, Expected Utility Maximization, Optimal Payoff, Benchmarks, Risk Measures, General / Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced mathematical theory, including optimal transport, Bregman divergences, and optimal payoff derivations under abstract constraints, indicating high math complexity. However, it lacks any empirical validation, backtests, or implementation details, focusing purely on theoretical results, resulting in low empirical rigor.

  flowchart TD
    A["Research Goal<br>Maximize Expected Utility under<br>Bregman-Wasserstein Constraint"] --> B["Methodology: Variation of<br>Calculus & Probabilistic Arguments"]
    B --> C{"Key Inputs & Parameters"}
    C --> D["Convex Generator φ<br>Determines Asymmetry"]
    C --> E["Benchmark Payoff X̃<br>Reference Outcome"]
    C --> F["Risk Parameter ε<br>Constraint Tolerance"]
    D & E & F --> G["Computational Process<br>Solve Euler-Lagrange Equation"]
    G --> H["Optimal Payoff Solution X*<br>Explicit Form via φ-Transform"]
    H --> I["Findings & Outcomes<br>Asymmetric Deviation Penalties<br>Customized Payoff Structures"]