Dynamic Programming in Convex Stochastic Optimization

This paper studies the dynamic programming principle for general convex stochastic optimization 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 noarbitrage 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.