|Start Page Number:||349|
|End Page Number:||388|
|Publication Date:||Jun 2017|
|Journal:||Mathematical Methods of Operations Research|
|Authors:||Menoukeu-Pamen Olivier, Momeya Romuald|
|Keywords:||markov processes, stochastic processes, control, optimization, simulation, investment|
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.