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Mean-Field Risk Sensitive Control and Zero-Sum Games for Markov Chains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2018 (English)Manuscript (preprint) (Other academic)
Abstract [en]

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. Using a Markov chain entropic backward SDE approach, we further 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.

Place, publisher, year, edition, pages
2018.
Keywords [en]
mean-field, nonlinear Markov chain, backward SDE, entropy, optimal control, risk sensitive, zero-sum game, saddle-point.
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-240112OAI: oai:DiVA.org:kth-240112DiVA, id: diva2:1269932
Funder
Swedish Research Council, 2016-04086
Note

QC 20181212

Available from: 2018-12-11 Created: 2018-12-11 Last updated: 2018-12-17Bibliographically approved
In thesis
1. Topics in Mean-Field Control and Games for Pure Jump Processes
Open this publication in new window or tab >>Topics in Mean-Field Control and Games for Pure Jump Processes
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is the collection of four papers addressing topics in stochastic optimal control, zero-sum games, backward stochastic differential equations, Pontryagin stochastic maximum principle and relaxed stochastic optimal control.

In the first two papers, we establish existence of Markov chains of mean-field type, with countable state space and unbounded jump intensities. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we derive conditions for existence of an optimal control and a saddle-point for a zero-sum differential game associated with risk-neutral and risk-sensitive payoff functionals of mean-field type, under dynamics driven by Markov chains of mean-field type. Our formulation of the control problems is of weak-type, where the dynamics are given in terms of a family of probability measures, under which the coordinate process is a pure jump process with controlled jump intensities.

In the third paper, we characterize the optimal controls obtained in the first pa-per by deriving sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP). Finally, within a completely different setup, in the fourth paper we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2018. p. 16
Series
TRITA-SCI-FOU ; 2018:55
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-240113 (URN)978-91-7873-061-2 (ISBN)
Public defence
2019-02-01, Kollegiesalen, Brinellvägen 8, Kungliga Tekniska högskolan, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2016-04086
Note

QC 20181212

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2018-12-13Bibliographically approved

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Choutri, Salah Eddine

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other locale
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Output format
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