On the stochastic maximum principle in optimal control of degenerate diffusions with lipschitz coefficients

Khaled Bahlali; Boualem Djehiche; Brahim Mezerdi

doi:10.1007/s00245-007-9017-6

On the stochastic maximum principle in optimal control of degenerate diffusions with lipschitz coefficients

Khaled Bahlali, Boualem Djehiche, Brahim Mezerdi

Mathematics

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

Abstract

We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space.

Original language	English (US)
Pages (from-to)	364-378
Number of pages	15
Journal	Applied Mathematics and Optimization
Volume	56
Issue number	3
DOIs	https://doi.org/10.1007/s00245-007-9017-6
State	Published - Dec 2007

Keywords

Degenerate diffusion
Optimal control
Stochastic differential equation
Stochastic maximum principle

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

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10.1007/s00245-007-9017-6

Cite this

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abstract = "We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space.",

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AU - Djehiche, Boualem

AU - Mezerdi, Brahim

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N2 - We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space.

AB - We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space.

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KW - Optimal control

KW - Stochastic differential equation

KW - Stochastic maximum principle

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On the stochastic maximum principle in optimal control of degenerate diffusions with lipschitz coefficients

Abstract

Keywords

ASJC Scopus subject areas

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