一般鞅驱动的倒向随机Volterra积分方程

doi:10.6040/j.issn.1671-9352.0.2014.041

山东大学学报（理学版） ›› 2014, Vol. 49 ›› Issue (07): 63-68.doi: 10.6040/j.issn.1671-9352.0.2014.041

一般鞅驱动的倒向随机Volterra积分方程

赵洁^1,3, 石玉峰^2,3

1. 中国人民银行菏泽市中心支行, 山东菏泽 274000;
2. 山东大学金融研究院, 山东济南 250100;
3. 山东大学数学学院, 山东济南 250100

收稿日期:2014-02-03 出版日期:2014-07-20 发布日期:2014-09-15
通讯作者: 石玉峰（1970- ），男，教授，博士，主要研究方向为随机分析、金融数学、随机控制、风险管理. E-mail：yfshi@sdu.edu.cn E-mail:yfshi@sdu.edu.cn
作者简介:赵洁（1986- ），女，硕士，主要研究方向为金融数学. E-mail：zhao.jie1227@163.com
基金资助:
国家自然科学基金资助项目（11371226，11071145,11231005）；国家自然科学基金委创新研究群体基金资助项目（11221061）；“111计划”资助项目（B12023）

Backward stochastic Volterra integral equations with general martingales

ZHAO Jie^1,3, SHI Yu-feng^2,3

1. The People's Bank of China Heze Central Subbranch, Heze 274000, Shandong, China;
2. Institute for Financial Studies, Shandong University, Jinan 250100, Shandong, China;
3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2014-02-03 Online:2014-07-20 Published:2014-09-15

摘要/Abstract

摘要： 证明了一般鞅驱动的倒向随机Volterra积分方程在Lipschitz假设条件下适应的M-解的存在唯一性，讨论了一般鞅驱动的线性倒向随机Volterra积分方程对应的对偶原理，并利用对偶原理证明了这类方程的比较定理。

关键词: 适应M-解, 对偶原理, 倒向随机Volterra积分方程

Abstract: The existence and uniqueness result of the adapted M-solution of backward stochastic Volterra integral equations (BSVIEs) driven by general martingales under Lipschitz conditions was proved, and the duality principles of the linear BSVIEs driven by general martingales were given. At last a comparison theorem of this kind of BSVIEs was showed by virtue of the duality principles.

Key words: adapted M-solution, Backward stochastic Volterra integral equation, duality principle

中图分类号:

O211.6

赵洁, 石玉峰. 一般鞅驱动的倒向随机Volterra积分方程[J]. 山东大学学报（理学版）, 2014, 49(07): 63-68.

ZHAO Jie, SHI Yu-feng. Backward stochastic Volterra integral equations with general martingales[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 63-68.

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一般鞅驱动的倒向随机Volterra积分方程

Backward stochastic Volterra integral equations with general martingales

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