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

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.

Keywords

• Backward stochastic Volterra integral equations
• existence
• uniqueness
• dynamic risk measure