A maximum principle for Markov regime-switching forward-backward stochastic differential games and applications

作者：Menoukeu Pamen Olivier^*; Momeya Romuald Herve

来源：Mathematical Methods of Operations Research, 2017, 85(3): 349-388.

DOI：10.1007/s00186-017-0574-4

• Forward-backward stochastic differential equations
• Markov regime-switching
• Stochastic differential games
• Optimal investment
• Stochastic maximum principle

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzero-sum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.

• 出版日期2017-6