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A Nonzero-sum game with reinforcement learning under mean-variance framework
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MAP20260001968
A Nonzero-sum game with reinforcement learning under mean-variance framework / Junyi Guo...[et al.]
Sumario: This paper examines a competitive setting in which two agents invest in a risk-free and a risky asset while considering both their own wealth and their wealth gap relative to each other. With market parameters partially or fully unknown, the problem is formulated as a nonzero-sum differential game within a reinforcement learning framework. Each agent seeks to optimize a Choquet-regularized, time-inconsistent mean-variance objective. Using dynamic programming, the authors derive a time-consistent Nash equilibrium in an incomplete market. Under a Gaussian mean-return assumption, they obtain an explicit analytical solution that enables the construction of a practical reinforcement learning algorithm. The algorithm shows uniform convergence, despite the absence of a traditional policy-improvement guarantee, and numerical experiments confirm its robustness and effectiveness
En: Astin bulletin. - Belgium : ASTIN and AFIR Sections of the International Actuarial Association = ISSN 0515-0361. - 19/01/2026 Volume 56 Issue 1 - January 2026 , p. 154 - 180
1. Mercados financieros ‌. 2. Gestión de riesgos ‌. 3. Modelo estocástico ‌. 4. Modelo Gaussiano ‌. 5. Cálculo actuarial ‌. 6. Matemática del seguro ‌. 7. Modelos matemáticos ‌. I. Guo, Junyi ‌. II. International Actuarial Association ‌. III. Title.