关键词: 分数阶Brown运动, 跳扩散, 随机微分方程, 随机最大值原理

Abstract:

Using classical variation method, we studied stochastic optimal control problem for stochastic differential equations driven by fractional Brownian motion with jumps and got stochastic maximum principle for the optimal control problem. The corresponding adjoint equations are shown to satisfy backward stochastic differential equation driven by fractional Brownian motion with jumps.

Key words: fractional Brownian motion, jump diffusion, stochastic differential equations, stochastic maximum principle