Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article
 


Journal of Convex Analysis 30 (2023), No. 4, 1241--1283
Copyright Heldermann Verlag 2023



Dynamic Programming in Convex Stochastic Optimization

Teemu Pennanen
Department of Mathematics, King's College London, United Kingdom
teemu.pennanen@kcl.ac.uk

Ari-Pekka Perkkiö
Mathematics Institute, Ludwig-Maximilian University, Munich, Germany
a.perkkioe@lmu.de



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 L1-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.

Keywords: Dynamic programming, stochastic programming, convexity.

MSC: 46N10, 90C39, 93E20.

[ Fulltext-pdf  (250  KB)] for subscribers only.