A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus
A Mean-Field Stochastic Maximum Principle for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps via Malliavin Calculus作者机构：School of Science Beijing University of Posts and Telecommunications Beijing China Department of Mathematics Anhui Normal University Wuhu China
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2018年第6卷第1期
页 面：138-154页
学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学]
主 题：Malliavin Calculus Maximum Principle Forward-Backward Stochastic Differential Equations Mean-Field Type Jump Diffusion Partial Information
摘 要：This paper considers a mean-field type stochastic control problem where the dynamics is governed by a forward and backward stochastic differential equation (SDE) driven by Lévy processes and the information available to the controller is possibly less than the overall information. All the system coefficients and the objective performance functional are allowed to be random, possibly non-Markovian. Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed.
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