由马氏链驱动的正倒向随机微分方程

doi:10.6040/j.issn.1671-9352.0.2017.483

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 46-54.doi: 10.6040/j.issn.1671-9352.0.2017.483

由马氏链驱动的正倒向随机微分方程

肖新玲

山东师范大学数学与统计学院, 山东济南 250014

收稿日期:2017-09-22 出版日期:2018-04-20 发布日期:2018-04-13
作者简介:肖新玲(1978— ),女,博士,研究方向为金融数学、金融管理与金融工程. E-mail:xinlingxiao@126.com
基金资助:
国家自然科学基金青年科学基金资助项目(11301309);山东师范大学教改项目(2016JG28);山东师范大学数学与统计学院青年专项基金资助项目(shxzhxxm201503)

Forward-backward stochastic differential equations on Markov chains

XIAO Xin-ling

School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, Shandong, China

Received:2017-09-22 Online:2018-04-20 Published:2018-04-13

摘要/Abstract

摘要： 主要研究由马氏链驱动的完全耦合的正倒向随机微分方程(forward-backward stochastic differential equation, FBSDE)解的存在唯一性;采用在研究通常的完全耦合的FBSDE时常用的连续性方法, 通过半鞅的Ito乘积法则与Lebesgue 控制收敛定理, 运用迭代法得到由马氏链驱动的完全耦合的FBSDE解的存在唯一性定理。

关键词: 解的存在唯一性, 马氏链, 正倒向随机微分方程

Abstract: In this paper, we mainly study the solutions about fully coupled forward-backward stochastic differential equations(FBSDE)on Markov chains. Using the usual method of continuation which is used to study fully coupled forward-backward stochastic differential equations, the Ito product rule of semimartingales, the Lebesgue control convergence theorem and iterative method, theorems about the solutions of the fully coupled forward-backward stochastic differential equations on Markov chains are obtained.

Key words: forward-backward stochastic differential equation, Markov chain, existence and uniqueness of solution

中图分类号:

O211.63

肖新玲. 由马氏链驱动的正倒向随机微分方程[J]. 山东大学学报（理学版）, 2018, 53(4): 46-54.

XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.

参考文献

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由马氏链驱动的正倒向随机微分方程

Forward-backward stochastic differential equations on Markov chains

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