Capacities, Measurable Selection and Dynamic Programming Part I: Abstract Framework

By Nicole El Karoui, Xiaolu Tan. 2013

72 citations recorded by the source corpus.

We give a brief presentation of the capacity theory and show how it derives naturally a measurable selection theorem following the approach of Dellacherie [11]. Then we present the classical method to prove the dynamic programming of discrete time stochastic control problem, using measurable selection arguments. At last, we propose a continuous time extension, that is an abstract framework for the continuous time dynamic programming principle (DPP).

Subfields: Economics and Econometrics, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/33d90b4acae41e22fd225d10a7ae9257b85fbcef

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Citations in the corpus

Stochastic control for a class of nonlinear kernels and applications (2015, background): “The problem in continuous-time has also been studied by El Karoui and Tan [40, 41], in a more general context than the previous references, but still based on the same arguments as in [35] and [65].”
Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems (2013, methodology): “In our accompanying paper [18], we have revisited the way how to deduce the measurable selection theorem by the capacity theory, where one of the basic ideas is to extend properties on the compact sets of a metric space to the Borel measurable sets by approximations.”