Dynamic Programming in Convex Stochastic Optimization

This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by R. T. Rockafellar and R. J-B Wets [Nonanticipativity and

-martingales in stochastic optimization problems, Math. Programming Studies 6 (1976) 170–187]. We extend the applicability of the theory by relaxing compactness and boundedness assumptions. In the context of financial mathematics, the relaxed assumptions are satisfied under the well-known no-arbitrage condition and the "reasonable asymptotic elasticity" condition of the utility function. Besides financial mathematics, we obtain several new results in linear and nonlinear stochastic programming and stochastic optimal control.