Maximum principle for robust utility optimization via Tsallis relative entropy

Paper: arXiv 2509.20888

Authors: Xueying Huang, Peng Luo, Dejian Tian

Abstract

This paper investigates an optimal consumption-investment problem featuring recursive utility via Tsallis relative entropy. We establish a fundamental connection between this optimization problem and a quadratic backward stochastic differential equation (BSDE), demonstrating that the value function is the value process of the solution to this BSDE. Utilizing advanced BSDE techniques, we derive a novel stochastic maximum principle that provides necessary conditions for both the optimal consumption process and terminal wealth. Furthermore, we prove the existence of optimal strategy and analyze the coupled forward-backward system arising from the optimization problem.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly rigorous theoretical analysis of robust utility optimization using Tsallis relative entropy, relying heavily on advanced BSDEs and stochastic maximum principles. However, as a purely mathematical finance paper, it lacks empirical backtests, empirical market data validation, or algorithmic code implementations.

Research Flowchart

  flowchart TD
    A[Goal: Robust Utility Optimization via Tsallis Relative Entropy] --> B[Inputs: Multi-Asset Market & Recursive Utility Model]
    B --> C[Establish Connection to Quadratic BSDE]
    C --> D[Derive Stochastic Maximum Principle]
    D --> E[Analyze Coupled Forward-Backward System]
    E --> F[Outcomes: Value Function Characterization & Optimal Strategy Existence]