Maximum principles for stochastic time-changed Volterra games

2020/12/11 by Giulia Di Nunno, Di Nunno, Giulia, Michele Giordano +1
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2012.06449

openalex publication_date 2020/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a stochastic differential game between two players, controlling a forward stochastic Volterra integral equation (FSVIE). Each player has to optimize his own performance functional which includes a backward stochastic differential equation (BSDE). The dynamics considered are driven by time-changed Lévy noises, with absolutely continuous time-change process. We prove a sufficient maximum principle to characterize Nash equilibria and the related optimal strategies. For this we use techniques of control under partial information, and the non-anticipating stochastic derivative. The zero-sum game is presented as a particular case.

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