  We study the existence of a solution for a one-dimensional generalized
backward stochastic differential equation with two reflecting barriers (GRBSDE
for short) under assumptions on the input data which are weaker than that on
the current literature. In particular, we construct a maximal solution for such
a GRBSDE when the terminal condition \xi is only F_T-measurable and the driver
f is continuous with general growth with respect to the variable y and
stochastic quadratic growth with respect to the variable z without assuming any
P-integrability conditions. The work is suggested by the interest the results
might have in Dynkin game problem and American game option.
