Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information
针对带跳的马尔可夫体制转换正倒向随机微分方程的最优控制问题，提出了三种最大值原理，包括一般充分型、等价型和基于Malliavin微积分的随机型，用于处理哈密顿函数非凹的情形，并应用于递归效用最大化问题。
This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward–backward stochastic differential equations with jumps. First, a general sufficient maximum principle for optimal control for a system, driven by a Markov regime-switching forward–backward jump–diffusion model, is developed. In the regime-switching case, it might happen that the associated Hamiltonian is not concave and hence the classical maximum principle cannot be applied. Hence, an equivalent type maximum principle is introduced and proved. In view of solving an optimal control problem when the Hamiltonian is not concave, we use a third approach based on Malliavin calculus to derive a general stochastic maximum principle. This approach also enables us to derive an explicit solution of a control problem when the concavity assumption is not satisfied. In addition, the framework we propose allows us to apply our results to solve a recursive utility maximization problem.