Mean-field risk sensitive control and zero-sum games for Markov chains

Salah Eddine Choutri; Boualem Djehiche

doi:10.1016/j.bulsci.2019.01.004

Mean-field risk sensitive control and zero-sum games for Markov chains

Salah Eddine Choutri, Boualem Djehiche

Mathematics

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

Abstract

We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Furthermore, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type. The conditions are derived using a Markov chain entropic backward SDE approach.

Original language	English (US)
Pages (from-to)	1-39
Number of pages	39
Journal	Bulletin des Sciences Mathematiques
Volume	152
DOIs	https://doi.org/10.1016/j.bulsci.2019.01.004
State	Published - May 2019

Keywords

Entropic backward SDE
Mean-field
Nonlinear Markov chain
Optimal control
Risk sensitive
Zero-sum game

ASJC Scopus subject areas

General Mathematics

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10.1016/j.bulsci.2019.01.004

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abstract = "We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Furthermore, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type. The conditions are derived using a Markov chain entropic backward SDE approach.",

keywords = "Entropic backward SDE, Mean-field, Nonlinear Markov chain, Optimal control, Risk sensitive, Zero-sum game",

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AU - Djehiche, Boualem

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AB - We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Furthermore, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with risk sensitive payoff functionals of mean-field type. The conditions are derived using a Markov chain entropic backward SDE approach.

KW - Entropic backward SDE

KW - Mean-field

KW - Nonlinear Markov chain

KW - Optimal control

KW - Risk sensitive

KW - Zero-sum game

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JF - Bulletin des Sciences Mathematiques

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Mean-field risk sensitive control and zero-sum games for Markov chains

Abstract

Keywords

ASJC Scopus subject areas

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