Maximum principles for stochastic time-changed Volterra games

Giulia Di Nunno; Michele Giordano

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arXiv · 2012.06449

Maximum principles for stochastic time-changed Volterra games

Giulia Di Nunno·Michele Giordano

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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 L\'evy 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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Giulia Di Nunno, Michele Giordano. 2020-12-11. Maximum principles for stochastic time-changed Volterra games. https://arxiv.org/abs/2012.06449

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