反映后向随机微分方程的动态规划方法

IF 1.3 3区 数学 Q2 STATISTICS & PROBABILITY
Hun O, Mun-Chol Kim, Kon-Gun Kim
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引用次数: 0

摘要

通过引入一类新的极小性条件,给出了求解含有càdlàg障碍物的反射倒向随机微分方程的一种新方法。我们的第一步是证明具有g期望的非线性最优停止问题的动态规划原理。然后利用g上鞅的非线性Doob-Meyer分解定理得到解的存在性。利用一种新的极小性条件,证明了RBSDEs解的一个有效表示公式。最后,我们得到了一些先验估计和稳定性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Dynamic programming approach to reflected backward stochastic differential equations
By introducing a new type of minimality condition, this paper gives a novel approach to the reflected backward stochastic differential equations (RBSDEs) with càdlàg obstacles. Our first step is to prove the dynamic programming principles for nonlinear optimal stopping problems with g-expectations. We then use the nonlinear Doob-Meyer decomposition theorem for g-supermartingales to get the existence of the solution. With a new type of minimality condition, we prove a representation formula of solutions to RBSDEs, in an efficient way. Finally, we derive some a priori estimates and stability results.
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来源期刊
Electronic Journal of Probability
Electronic Journal of Probability 数学-统计学与概率论
CiteScore
1.80
自引率
7.10%
发文量
119
审稿时长
4-8 weeks
期刊介绍: The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.
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