Maximum principles for stochastic time-changed Volterra games
Probability
2023-03-07 v2 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2012.06449,
title = {Maximum principles for stochastic time-changed Volterra games},
author = {Giulia Di Nunno and Michele Giordano},
journal= {arXiv preprint arXiv:2012.06449},
year = {2023}
}