Paper: arXiv 2603.20580

Authors: Silvana M. Pesenti, Thai Nguyen

Abstract

We consider the problem of active portfolio management, where an investor seeks the portfolio with maximal expected utility of the difference between the terminal wealth of their strategy and a proportion of the benchmark’s, subject to a budget and a deviation constraint from the benchmark portfolio. As the investor aims at outperforming the benchmark, they choose a divergence that asymmetrically penalises gains and losses as well as penalises underperforming the benchmark more than outperforming it. This is achieved by the recently introduced $α$-Bregman-Wasserstein divergence, subsuming the Bregman-Wasserstein and the popular Wasserstein divergence. We prove existence and uniqueness, characterise the optimal portfolio strategy, and give explicit conditions when the divergence constraints and the budget constraints are binding. We conclude with a numerical illustration of the optimal quantile function in a geometric Brownian motion market model.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework introducing the alpha-Bregman Wasserstein divergence to portfolio optimization with benchmark constraints. While the mathematical derivation, proofs of existence, and optimal portfolio characterization are sophisticated and novel, the paper relies primarily on a stylized numerical illustration rather than empirical backtesting against real market data.

Research Flowchart

  flowchart TD
    A[Research Goal: Maximize utility vs. benchmark using asymmetric divergence constraint] --> B[Model Inputs: Budget, Market Model GBM, & α-Bregman-Wasserstein Divergence]
    B --> C[Formulate Optimization: Maximizing terminal wealth difference under constraints]
    C --> D[Theoretical Analysis: Prove existence, uniqueness, & binding conditions]
    D --> E[Numerical Simulation: Evaluate optimal quantile function in GBM market]
    E --> F[Outcomes: Characterized optimal active portfolio strategy asymmetric to benchmark]

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3 of 65 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.