We prove an existence and uniqueness theorem for backward stochastic differential equations driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one.

We apply theoretical results by Peng on supersolutions for Backward SDEs (BSDEs) to the problem of finding optimal superhedging strategies in a generalized Black-Scholes market under constraints. Constraints may be imposed simultaneously on wealth process and portfolio. They may be non-convex,...