On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Mario Annunziato; Alfio Borzì; Fabio Nobile; Raul Tempone

doi:10.4236/am.2014.516239

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Mario Annunziato, Alfio Borzì, Fabio Nobile, Raul Tempone

Research output: Contribution to journal › Article › peer-review

Abstract

In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.

Original language	English (US)
Pages (from-to)	2476-2484
Number of pages	9
Journal	Applied Mathematics
Volume	05
Issue number	16
DOIs	https://doi.org/10.4236/am.2014.516239
State	Published - Sep 2 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Supported in part by the European Union under Grant Agreement “Multi-ITN STRIKE-Novel Methods in Computational Finance”. Fund Project No. 304617 Marie Curie Research Training Network.

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10.4236/am.2014.516239

https://repository.kaust.edu.sa/bitstream/10754/336769/1/AM_2014090214433651.pdf

Cite this

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title = "On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks",

abstract = "In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.",

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AU - Tempone, Raul

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AB - In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assumptions it is shown that the two strategies are equivalent in the case of expected cost functionals, while the FokkerPlanck formalism allows considering a larger class of objectives. To illustrate the connection between the two control strategies, the cases of an Itō stochastic process and of a piecewise-deterministic process are considered.

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On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

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