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arXiv · 2509.20888

Maximum principle for robust utility optimization via Tsallis relative entropy

Xueying Huang·Peng Luo·Dejian Tian
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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.

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Xueying Huang, Peng Luo, Dejian Tian. 2025-09-25. Maximum principle for robust utility optimization via Tsallis relative entropy. https://arxiv.org/abs/2509.20888

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