Maximum principles for stochastic time-changed Volterra games

TL;DR

This paper develops maximum principles for stochastic time-changed Volterra games involving two players optimizing their strategies in a complex stochastic environment driven by time-changed Lévy noises, with applications to Nash equilibria.

Contribution

It introduces a sufficient maximum principle for Nash equilibria in stochastic Volterra games with time-changed Lévy noise, extending control theory under partial information.

Findings

Established a maximum principle for Nash equilibria.

Characterized optimal strategies in stochastic Volterra games.

Extended control techniques to time-changed Lévy noise environments.

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.