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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

Ari-Pekka Perkkiö
Mathematics Institute, Ludwig-Maximilian University, Munich, Germany

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.

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