Stochastic optimization under constraints

We study a stochastic optimization problem under constraints in a general f ramework including financial models with constrained portfolios, labor inco me and large investor models and reinsurance models. We also impose America n-type constraint on the state space process. General objective functions i ncluding deterministic or random utility functions and shortfall risk loss functions are considered We first prove existence and uniqueness result to this optimization problem. In a second part, we develop a dual formulation under minimal assumptions on the objective functions, which are the analogu e of the asymptotic elasticity condition of Kramkov and Schachermayer (1999 ). (C) 2001 Elsevier Science B.V. All rights reserved.