A stochastic maximum principle for markov chains of mean-field type

Salah Eddine Choutri; Tembine Hamidou

doi:10.3390/g9040084

A stochastic maximum principle for markov chains of mean-field type

Salah Eddine Choutri, Tembine Hamidou

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

Abstract

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications.

Original language	English (US)
Article number	84
Journal	Games
Volume	9
Issue number	4
DOIs	https://doi.org/10.3390/g9040084
State	Published - Dec 2018

Keywords

Backward sdes
Mean-field
Nonlinear markov chain
Optimal control
Stochastic maximum principle

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.3390/g9040084

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AB - We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type which are pure jump processes obtained as solutions of a well-posed martingale problem. As an illustration, we apply the result to generic examples of control problems as well as some applications.

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KW - Nonlinear markov chain

KW - Optimal control

KW - Stochastic maximum principle

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A stochastic maximum principle for markov chains of mean-field type

Abstract

Keywords

ASJC Scopus subject areas

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