数学物理学报(英文版) ›› 2013, Vol. 33 ›› Issue (5): 1407-1418.doi: 10.1016/S0252-9602(13)60092-2

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INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS

贾广岩|张娜*   

  1. Qilu Securities Institute for Financial Studies, Shandong University, Jinan 250199, China； College of Management and Economics, Tianjin University, Tianjin 300072, China；China Center for Social Computing, Tianjin University, Tianjin 300072, China
  • 收稿日期:2011-08-31 修回日期:2012-02-22 出版日期:2013-09-20 发布日期:2013-09-20
  • 通讯作者: 张娜，znna1225@163.com E-mail:jiagy@sdu.edu.cn；znna1225@163.com
  • 基金资助:

    The authors thank the partial support from the NSF of China (11171186), the NSF of Shandong Province(ZR2010AM021) and the “111” project.

INVARIANT REPRESENTATION FOR STOCHASTIC DIFFERENTIAL OPERATOR BY BSDES WITH UNIFORMLY CONTINUOUS COEFFICIENTS AND ITS APPLICATIONS

 JIA Guang-Yan, ZHANG Na*   

  1. Qilu Securities Institute for Financial Studies, Shandong University, Jinan 250199, China； College of Management and Economics, Tianjin University, Tianjin 300072, China；China Center for Social Computing, Tianjin University, Tianjin 300072, China
  • Received:2011-08-31 Revised:2012-02-22 Online:2013-09-20 Published:2013-09-20
  • Contact: ZHANG Na，znna1225@163.com E-mail:jiagy@sdu.edu.cn；znna1225@163.com
  • Supported by:

    The authors thank the partial support from the NSF of China (11171186), the NSF of Shandong Province(ZR2010AM021) and the “111” project.

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摘要：

In this paper, we prove that a kind of second order stochastic differential op-erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continu-ous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated so-lutions of BSDEs. Moreover, we give a new proof about g-convexity.

关键词: backward stochastic differential equations, stochastic differential operators, representation theorems, converse comparison theorem

Abstract:

In this paper, we prove that a kind of second order stochastic differential op-erator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continu-ous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated so-lutions of BSDEs. Moreover, we give a new proof about g-convexity.

Key words: backward stochastic differential equations, stochastic differential operators, representation theorems, converse comparison theorem

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  • 60H10
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