-estimate for mean-field type FBSDEs

This paper is concerned with the Lp-regularity (p > 2) of mean-field type forward–backward stochastic differential equations (MF-FBSDEs, for short). For three classes of nonlinear MF-FBSDEs, linear MF-FBSDEs and linear Hamiltonian systems, we obtain three Lp-results, respectively. Each Lp-result includes the existence, estimate and continuous dependence on parameters of solutions in the sense of p-th power integrability. In the third case, we also provide an Lp-result for the optimal controls of a class of mean-field type linear-quadratic (MF-LQ, for short) problems with random coefficient matrices.