Abstract

A type of forward-backward doubly stochastic differential equations driven by Brownian motions and Poisson process (FBDSDEP) is studied. Under some monotonicity assumptions, the existence and uniqueness results for measurable solutions of FBDSDEP are established via a method of continuation. Then the continuity and differentiability of the solutions to FBDSDEP depending on parameters is discussed. Furthermore, these results were applied to backward doubly stochastic linear quadratic (LQ) nonzero sum differential games with random jumps to get the explicit form of the open–loop Nash equilibrium point by the solution of the FBDSDEP.

个人简介：朱庆峰，山东财经大学副教授和硕士研究生导师。入选山东财经大学首批青年优秀人才支持计划，作为学术带头人入选山东财经大学首批优势学科人才团队计划。担任国家自然科学基金通信评审专家，山东省应用统计学会理事以及多个SCI源期刊审稿人。研究领域涉及随机控制、随机分析、金融数学等。发表论文涉及《ESAIM: Control, Optimisation and Calculus of Variations》，《IEEE Trans. Automat. Control》，《Science China Mathematics》等杂志。