Generalized Backward Stochastic Differential Equation With Two Reflecting Barriers and Stochastic Quadratic Growth

In this paper we study one-dimensional generalized reflected backward stochastic differential equation with two barriers and stochastic quadratic growth. We prove the existence of a maximal solution when there exists a semimartingale between the barriers L and U , the generator f is continuous with general growth with respect to the variable y and stochastic quadratic growth with respect to the variable z and without assuming any P -integrability conditions on the data. The proof of our result is based on the use of a comparison theorem, an exponential transformation and an approximation technique. Our result is applied to the Dynkin game problem as well as to the American game option. Keys Words: Reflected backward stochastic differential equation; stochastic quadratic growth; comparison theorem; exponential transformation. AMS Classification(1991): 60H10, 60H20.