A Maximum Principle for Markov Regime-Switching Forward Backward   Stochastic Differential Games and Applications
  In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward-backward stochastic differential equations with jumps and partial information. First, we prove a sufficient maximum principle for non zero-sum stochastic differential game problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for non zero-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 penalty entropy. We also apply the result to find optimal investment of an insurance firm under model uncertainty. 
Olivier Menoukeu Pamen and Romual Herve Momeya
math.OC