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Maximum principle for robust utility optimization via Tsallis relative entropy

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  • 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.

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  • Xueying Huang & Peng Luo & Dejian Tian, 2025. "Maximum principle for robust utility optimization via Tsallis relative entropy," Papers 2509.20888, arXiv.org.
    • Handle: RePEc:arx:papers:2509.20888
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    File URL: http://arxiv.org/pdf/2509.20888
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