General Mean-Field BDSDEs with Stochastic Linear Growth and Discontinuous Generator

Abstract

In this paper, we consider the general mean-field backward doubly stochastic differential equations (mean-field BDSDEs) whose generator f can be discontinuous in y. We prove the existence theorem of solutions under stochastic linear growth conditions and also obtain the related comparison theorem. Naturally, we present those results under the linear growth condition, which is a special case of the stochastic condition. Finally, a financial claim sale problem is discussed, which demonstrates the application of the general mean-field BDSDEs in finance.

Keywords

• backward doubly stochastic differential equations
• mean-field
• Wasserstein metric
• discontinuous
• stochastic linear growth