由Lévy过程驱动的一类特殊的高维的BSRDE解的存在唯一性

Existence and Uniqueness of a Class of Special Multi-dimensional BSRDE Driven by Levy Processes

讨论由Brownian运动和Lévy过程共同驱动的线性随机系统的随机LQ问题,其中代价泛函是关于Lévy过程生成的σ-代数取条件期望.得到由Lévy过程驱动的新的多维的倒向随机Riccati方程,利用Bellman拟线性原理和单调收敛方法证明了此随机Riccati方程的解的存在性.

In this paper, we investigate the stochastic linear-quadratic optimal control prob- lem for the linear stochastic system driven by both Brownian motions and Ldvy processes, where the cost functional takes conditional expectation with respect to the a-algebras gen- erated by Lévy processes. We obtain the new multidimensional backward stochastic Riccati differential equation driven by Lévy processes and prove the existence of solutions of this stochastic Riccati equation using Bellman＇s quasilinear principle and a method of monotone convergence.