Capacities, Measurable Selection and Dynamic Programming Part II: Application in Stochastic Control Problems
By Nicole El Karoui, Xiaolu Tan. 2013
102 citations recorded by the source corpus.
We aim to give an overview on how to derive the dynamic programming principle for a general stochastic control/stopping problem, using measurable selection techniques. By considering their martingale problem formulation, we show how to check the required measurability conditions for different versions of control/stopping problem, including in particular the controlled/stopped diffusion processes problem. Further, we also study the stability of the control problem, i.e. the approximation of the control process by piecewise constant control problems. It induces in particular an equivalence result for different versions of the controlled/stopped diffusion processes problem.
Subfields: Economics and Econometrics, Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/f497d4ee124dc091ef90e134936d842319ccd7a8
How researchers see this paper
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In Economics and Econometrics
- Jianfeng Zhang
- Dylan Possamaï
- Cong Wu
- Daniel Lacker
- Xiaolu Tan
- Markus Fischer
- Marcel Nutz
- Franccois Delarue
In Finance
- Dylan Possamaï
- Jianfeng Zhang
- Cong Wu
- Xiaolu Tan
- Daniel Lacker
- Chao Zhou
- Marcel Nutz
- Jean-François Chassagneux
In Management Science and Operations Research
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].”
- A general characterization of the mean field limit for stochastic differential games (2014, background): “5 will elaborate on this point, and see also [24] or the more recent [26] for further dicussion.”
- Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls (2018, methodology): “rogramming principle and the viscosity property. It will be interesting to know if one can circumvent the regularity issue by establishing the DPP using measurable selection as in El Karoui & Tan [19, 20]. (ii) However, for zero-sum games, the open-loop controls and closed-loop controls are quit”