Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps
Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps
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DOI：
10.1137/080739781
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发表时间：
2009-11
期刊：
影响因子：
--
通讯作者：
B. Øksendal;A. Sulem
中科院分区：
文献类型：
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作者：
B. Øksendal;A. Sulem
给出了带跳的正反向随机微分方程最优控制的最大值原理的不同形式。我们的研究的动机是通过$g$预期将风险降至最低。首先证明了由Levy过程驱动的前向和后向随机系统在部分信息下的最优控制的一般充分极大值原理。然后，我们提出了一种Malliavin微积分方法，它允许我们处理非马尔可夫系统。最后，给出了应用实例。
We present various versions of the maximum principle for optimal control of forward-backward stochastic differential equations (SDE) with jumps. Our study is motivated by risk minimization via $g$-expectations. We first prove a general sufficient maximum principle for optimal control with partial information of a stochastic system consisting of a forward and a backward SDE driven by Levy processes. We then present a Malliavin calculus approach which allows us to handle non-Markovian systems. Finally, we give examples of applications.