Dynamic programming in convex stochastic optimization

TL;DR

This paper extends the dynamic programming principle for convex stochastic optimization by relaxing key assumptions, broadening its applicability in finance, stochastic programming, and control.

Contribution

It generalizes the theory of convex stochastic optimization by removing compactness and boundedness constraints, applicable under no-arbitrage and elasticity conditions.

Findings

Broadened the applicability of dynamic programming in finance and control

Established new results in linear and nonlinear stochastic programming

Validated assumptions under well-known financial conditions

Abstract

This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness assumptions. In the context of financial mathematics, the relaxed assumption 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.