RBSDEs with stochastic monotone and polynomial growth condition (Q938574)

Existence and uniqueness of solutions of two problems are attacked in the paper: First a backward stochastic differential equation \(Y_t=\xi+\int_t^Tf(s,Y_s,Z_s)\,ds-\int_t^TZ_s\,dW_s\) with given data \((T,\xi,W)\) where \(T\) is the terminal time, \(\xi\) is the terminal state, \(W\) is a Brownian motion and \((Y,Z)\) are the unknowns, and, second, a reflected backward stochastic differential equation \(Y_t=\xi+\int_t^Tf(s,Y_s,Z_s)\,ds-\int_t^TZ_s\,dW_s+K_T-K_t\) with given data \((T,\xi,W)\) as above and the unknowns \((Y,Z,K)\). The reflection is realized through two additional conditions upon the solution: first \(Y\in Dom(\Phi)\) where \(\Phi\) is a given lower-semicontinuous and convex function, and, second, an integral condition connecting, in a specific way, the process \(K\) with the subdifferential of \(\Phi\). The drift function \(f=f(\omega,s,y,z)\) is assumed to be random, monotone in \(y\) and Lipschitz in \(z\).