G-Backward Stochastic Diferential Equations with Random Terminal Times

this paper, we study G-backward stochastic differential equations with random terminal times. We explain how to extend the results of the case of fixed terminal time to the case of a random terminal time. We present the existence and uniqueness of a solution for G-backward stochastic differential equations with a random terminal time. We consider the G-backward stochastic differential equations with the random terminal time in the following form (7) , Where is a stopping time with respect to natural filtration , the processes , and are unknown and the random functions and , said generators, and the random variable , said terminal value, are given. The process 0 is called a G-Brownian motion. We present the existence and uniqueness of a solution for G-BSDE (7).

Keywords:

G-Expectation , G-Brownian motion , G-Backward stochastic differential equations , Random terminal times