Journal Article10.1287/MOOR.1.3.267
Measurable Selection and Dynamic Programming
TL;DR: A general multistage problem of stochastic optimization is studied and under some simple assumptions that the extremum in the problem is attained and a criterion of optimality in terms of these Bellman functions is given.
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Abstract: A general multistage problem of stochastic optimization is studied. It is proved under some simple assumptions that the extremum in the problem is attained. The “Bellman functions” are constructed and a criterion of optimality in terms of these functions is given. The main tools used are measurable selection theorems. The paper generalizes the previous work of R. T. Rockafellar and R. J.-B. Wets devoted to the convex case.
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Citations
Survey of Measurable Selection Theorems
TL;DR: In this article, Kuratowski and Ryll-Nardzewski showed that the existence off problem can be solved by lifting F in a natural way to a map into the closed sets of a Polish space.
610
Nonanticipativity and L1-martingales in stochastic optimization problems
R. T. Rockafellar,Roger J.-B. Wets +1 more
- 01 Jan 1976
TL;DR: In this paper, necessary and sufficient conditions for optimality are derived for multistage stochastic programs under some standard regularity conditions and a condition of non-anticipative feasibility.
169
On utility maximization in discrete-time financial market models
Miklós Rásonyi,Lukasz Stettner +1 more
TL;DR: In this article, the authors consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility.
Measurable selection theorems for optimization problems
TL;DR: In this article, the authors attempt a unification of several selection theorems in the literature by introducing the notion of a selection class and give sufficient conditions for the existence of measurable e-maximizers.
82
On utility maximization in discrete-time financial market models
Miklós Rásonyi,Lukasz Stettner +1 more
TL;DR: In this paper, the authors consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility.
75
References
Convex Integral Functionals and Duality
R. Tyrrell Rockafellar
- 01 Jan 1971
TL;DR: The duality of convex integral functions has been studied extensively in the literature, see as discussed by the authors for a survey. But the duality has not yet been considered in the analysis of general convex functions.
129
Stochastic Programs with Recourse II: On the Continuity of the Objective
David W. Walkup,Roger J.-B. Wets +1 more
TL;DR: In this article, it was shown that the objective of stochastic programs with recourse is also lower semi-continuous and a lemma of general interest in the theory of convex functions is established.
34
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