The maximum principle for fully coupled forward-backward stochastic control system with state constraints;

Optimal control problems of forward backward stochastic systems with nonsmooth cost functionals are studied and a necessary condition for optimal control is obtained by convex variational method and Ekeland s variational principle.

using relevant linear forward-backward stochastic differential equations, it obtains a calculating formula of the retained proportion or retention for the reinsurance.

Starting from systematic view,the paper integrates compensations that insuers will be up against with its return on investment and establishes linear forward-backward stochastic differential equations for proportional and excess-of-loss reinsurance premiums.

The well-posedness of time-delayed forward-backward stochastic differential equations is studied.

In this paper, we investigate the nature of the adapted solution to a class of forward-backward stochastic differential equations (short for FBSDE) without the non-degenerate condition for the forward equation.