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 nonzerosum 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.Keywords Forward-backward stochastic differential equations · Markov regimeswitching · Stochastic differential games · Optimal investment · Stochastic maximum principleThe project on which this publication is based has been carried out with funding
This paper deals with the characterization problem of the minimal entropy martingale measure (MEMM) for a Markov-modulated exponential Lévy model. This model is characterized by the presence of a background process modulating the risky asset price movements between different regimes or market environments. This allows to stress the strong dependence of financial assets price with structural changes in the market conditions. Our main results are obtained from the key idea of working conditionally on the modulator-factor process. This reduces the problem to studying the simpler case of processes with independent increments. Our work generalizes some previous works in the literature dealing with either the exponential Lévy case or the exponential-additive case.
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