arXiv:2611.13051v1 Announce Type: new Abstract: This paper studies the well-posedness of mean-field backward stochastic differential equations (BSDEs, for short) with Poisson jumps, where the generator has quadratic growth with respect to $Z$ and exponential growth with respect to $U$, where $(Y,Z,U)$ denotes the solution of this BSDE. First, we prove the existence and the uniqueness of local solutions to mean-field backward stochastic differential equations with jumps (BSDEJs, for short) by using a fixed-point argument. Then, based on these local results, we discuss the solvability of global solutions in the following two cases: in the first one, the generator has linear growth with respect to $Y$ and the corresponding marginal distribution $\mu_1$; and in the second one, the generator has subquadratic growth with respect to the marginal distribution $\mu_2$ and linear growth with respect to the marginal distribution $\mu_3$, corresponding to $Z$ and $U$, respectively. Finally, by employing a Girsanov transformation we establish a comparison theorem for mean-field BSDEJs under quadratic-exponential growth conditions.
Continue to arXiv Mathematics →You are being forwarded in 6s — stay on this page