Geodesic
Dynamic Programming in Convex Stochastic Optimization
Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1241-1283
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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.
Classification : 46N10, 90C39, 93E20
Mots-clés : Dynamic programming, stochastic programming, convexity 
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     title = {Dynamic {Programming} in {Convex} {Stochastic} {Optimization}},
     journal = {Journal of convex analysis},
     pages = {1241--1283},
     year = {2023},
     volume = {30},
     number = {4},
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T. Pennanen; A.-P. Perkkiö. Dynamic Programming in Convex Stochastic Optimization. Journal of convex analysis, Tome 30 (2023) no. 4, pp. 1241-1283. http://geodesic.mathdoc.fr/item/JCA_2023_30_4_JCA_2023_30_4_a7/