Maximum principle for robust utility optimization via Tsallis relative entropy

Xueying Huang, Peng Luo and 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.

Date: 2025-09
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2509.20888

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