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,...

We consider a financial market in which the discounted price process S is an ℝd-valued semimartingale with bounded jumps, and the variance-optimal martingale measure (VOMM) Qopt is only known to be a signed measure. We give a backward semimartingale equation (BSE) and show that the density...

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,...

We consider the mean-variance hedging of a contingent claim H when the discounted price process S is an [image omitted]-valued quasi-left continuous semimartingale with bounded jumps. We relate the variance-optimal martingale measure (VOMM) to a backward semimartingale equation (BSE) and show...

We consider an optimal control problem for an Itô diffusion and a related stopping problem. Their value functions satisfy (d/dx)V=u and an optimal control defines an optimal stopping time. Conversely, we construct an optimal control from optimal stopping times, find a representation of V as an...

We provide a method for solving dynamic expected utility maximization problems with possibly not everywhere increasing utility functions in an Lp-semimartingale setting. In particular, we solve the problem for utility functions of type (exponential problem) and (2m-th problem). The convergence...

It is well known that backward stochastic differential equations (BSDEs) stem from the study on the Pontryagin type maximum principle for optional stochastic control. A solution of a BSDE hits a given terminal value (which is a random variable) by virtue of an additional martingale term and an...

The existence of an adapted solution to a backward stochastic differential equation which is not adapted to the filtration of the underlying Brownian motion is proved. This result is applied to the pricing of contingent claims. It allows to compare the prices of agents who have different...