Mean-field backward stochastic differential equations and applications

In this paper we study the linear mean-field backward stochastic differential equations (mean-field BSDE) of form (0.1) d Y ( t ) = − [ α 1 + β Z ∫ R 0 η , ζ K ν 2 E ] γ B N ̃ ∈ T ξ . where is unknown solution triplet, a Brownian motion, compensated Poisson random measure, independent We prove existence and uniqueness triplet such systems. Then give an explicit formula for first component by using partial Malliavin derivatives. To illustrate our result apply them to recursive utility optimization problem in finance.