A Nonzero Sum Differential Game of BSDE With Time-Delayed Generator and Applications

In this technical note, a nonzero sum differential game is studied, where the state dynamics follows a backward stochastic differential equation with time-delayed generator. An Arrow's sufficient condition for open-loop equilibrium point is proved. A linear-quadratic differential game and a pension fund management problem with time-delayed surplus are discussed as the applications of the sufficient optimality condition.