Lp-estimate for mean-field type FBSDEs

This paper is concerned with the $L^p$-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 $L^p$-results, respectively. Each $L^p$-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 $L^p$-result for the optimal controls of a class of mean field type linear-quadratic (MF-LQ, for short) problems with random coefficient matrices.