Dynamic programming in convex stochastic optimization

Teemu Pennanen; Ari-Pekka Perkkio

Dynamic programming in convex stochastic optimization

Teemu Pennanen, Ari-Pekka Perkkio

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Abstract

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.

Original language	English
Pages (from-to)	1241-1283
Journal	JOURNAL OF CONVEX ANALYSIS
Volume	30
Issue number	2
Publication status	Published - 5 May 2023

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https://www.heldermann.de/JCA/JCA30/JCA304/jca30056.htm

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title = "Dynamic programming in convex stochastic optimization",

abstract = "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.",

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AB - 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.

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JO - JOURNAL OF CONVEX ANALYSIS

JF - JOURNAL OF CONVEX ANALYSIS

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ER -

Dynamic programming in convex stochastic optimization

Abstract

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