In an arbitrage free incomplete market we consider the problem of maximizing terminal isoelastic utility. The relationship between the optimal portfolio, the optimal martingale measure in the dual problem and the optimal value function of the problem is described by an BSDE. For a totally...

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...