Electron. J. Diff. Equ., Vol. 2014 (2014), No. 178, pp. 1-16.

Existence and uniqueness of M-solutions for backward stochastic Volterra integral equations

Wenxue Li, Ruihua Wu, Ke Wang

Abstract:
In this article, we study general backward stochastic Volterra integral equations (BSVIEs). Combining the contractive-mapping principle, step-by-step iteration method and mathematical induction, we establish the existence and uniqueness theorem of M-solution for the BSVIEs. This theorem could be applied directly to many models, for example, using the result to a kind of financial models provides a new and easy method to discuss the existence of dynamic risk measure.

Submitted August 2, 2013. Published August 21, 2014.
Math Subject Classifications: 45D05, 60H17, 34A12, 60H20.
Key Words: Backward stochastic Volterra integral equations; existence; uniqueness; dynamic risk measure.

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Wenxue Li
Department of Mathematics
Harbin Institute of Technology (Weihai)
Weihai 264209, China
Phone +86 0631 5687035, fax +86 0631 5687572
email: wenxuetg@hitwh.edu.cn
Ruihua Wu
Department of Mathematics
Harbin Institute of Technology (Weihai)
Weihai 264209, China
email: wu_ruihua@hotmail.com
Ke Wang
Department of Mathematics
Harbin Institute of Technology (Weihai)
Weihai 264209, China
email: wangke@hitwh.edu.cn

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