Dynamic Programming in Convex Stochastic Optimization

Perkkiö, Ari-Pekka und Pennanen, Teemu (2023): Dynamic Programming in Convex Stochastic Optimization. In: Journal of Convex Analysis, Bd. 30, Nr. 4: S. 1241-1283

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch