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On relaxed stochastic optimal control for stochastic differential equations driven by G-Brownian motion
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
2018 (English)In: Latin American Journal of Probability and Mathematical Statistics, ISSN 1980-0436, E-ISSN 1980-0436, Vol. 15, no 1, p. 201-212Article in journal (Refereed) Published
Abstract [en]

In the G-framework, we establish existence of an optimal stochastic relaxed control for stochastic differential equations driven by a G-Brownian motion.

Place, publisher, year, edition, pages
Instituto Nacional de Matematica Pura e Aplicada , 2018. Vol. 15, no 1, p. 201-212
Keywords [en]
Capacity, G-Brownian motion, G-chattering lemma, Relaxed optimal control, Sublinear expectation
National Category
Probability Theory and Statistics
Research subject
Applied and Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-238436DOI: 10.30757/ALEA.v15-09ISI: 000460472300009Scopus ID: 2-s2.0-85052941773OAI: oai:DiVA.org:kth-238436DiVA, id: diva2:1259814
Note

QC 20181031

Available from: 2018-10-31 Created: 2018-10-31 Last updated: 2019-03-27Bibliographically 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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