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Choutri, S. E. & Djehiche, B. (2019). Mean-field risk sensitive control and zero-sum games for Markov chains. Bulletin des Sciences Mathématiques, 152, 1-39
Open this publication in new window or tab >>Mean-field risk sensitive control and zero-sum games for Markov chains
2019 (English)In: Bulletin des Sciences Mathématiques, ISSN 0007-4497, E-ISSN 1952-4773, Vol. 152, p. 1-39Article in journal (Refereed) Published
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. 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.

Place, publisher, year, edition, pages
Elsevier Masson SAS, 2019
Keywords
Entropic backward SDE, Mean-field, Nonlinear Markov chain, Optimal control, Risk sensitive, Zero-sum game
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-246443 (URN)10.1016/j.bulsci.2019.01.004 (DOI)2-s2.0-85060571662 (Scopus ID)
Note

QC 20190319

Available from: 2019-03-19 Created: 2019-03-19 Last updated: 2019-03-19Bibliographically approved
Aurell, A. & Djehiche, B. (2019). Modeling tagged pedestrian motion: A mean-field type game approach. Transportation Research Part B: Methodological, 121, 168-183
Open this publication in new window or tab >>Modeling tagged pedestrian motion: A mean-field type game approach
2019 (English)In: Transportation Research Part B: Methodological, ISSN 0191-2615, E-ISSN 1879-2367, Vol. 121, p. 168-183Article in journal (Refereed) Published
Abstract [en]

This paper suggests a model for the motion of tagged pedestrians: Pedestrians moving towards a specified targeted destination, which they are forced to reach. It aims to be a decision-making tool for the positioning of fire fighters, security personnel and other services in a pedestrian environment. Taking interaction with the surrounding crowd into account leads to a differential nonzero-sum game model where the tagged pedestrians compete with the surrounding crowd of ordinary pedestrians. When deciding how to act, pedestrians consider crowd distribution-dependent effects, like congestion and crowd aversion. Including such effects in the parameters of the game, makes it a mean-field type game. The equilibrium control is characterized, and special cases are discussed. Behavior in the model is studied by numerical simulations.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Backward-forward stochastic differential equations, Congestion, Crowd aversion, Evacuation planning, Mean-field type games, Pedestrian dynamics
National Category
Transport Systems and Logistics
Identifiers
urn:nbn:se:kth:diva-246491 (URN)10.1016/j.trb.2019.01.011 (DOI)2-s2.0-85060867885 (Scopus ID)
Note

QC 20190319

Available from: 2019-03-19 Created: 2019-03-19 Last updated: 2019-03-19Bibliographically approved
Choutri, S. e., Djehiche, B. & Tembine, H. (2019). OPTIMAL CONTROL AND ZERO-SUM GAMES FOR MARKOV CHAINS OF MEAN-FIELD TYPE. Mathematical Control and Related Fields, 9(3), 571-605
Open this publication in new window or tab >>OPTIMAL CONTROL AND ZERO-SUM GAMES FOR MARKOV CHAINS OF MEAN-FIELD TYPE
2019 (English)In: Mathematical Control and Related Fields, ISSN 2156-8472, E-ISSN 2156-8499, Vol. 9, no 3, p. 571-605Article in journal (Refereed) Published
Abstract [en]

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, 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 payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.

Place, publisher, year, edition, pages
AMER INST MATHEMATICAL SCIENCES-AIMS, 2019
Keywords
Mean-field, nonlinear Markov chain, backward SDEs, optimal control, zero-sum game, saddle point, stochastic maximum principle, thinning
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-251267 (URN)10.3934/mcrf.2019026 (DOI)000465287600008 ()
Note

QC 20190513

Available from: 2019-05-13 Created: 2019-05-13 Last updated: 2019-05-13Bibliographically approved
Djehiche, B. & Löfdahl, B. (2018). A Hidden Markov Approach to Disability Insurance. North American Actuarial Journal, 22(1), 119-136
Open this publication in new window or tab >>A Hidden Markov Approach to Disability Insurance
2018 (English)In: North American Actuarial Journal, ISSN 1092-0277, E-ISSN 2325-0453, Vol. 22, no 1, p. 119-136Article in journal (Refereed) Published
Abstract [en]

Point and interval estimation of future disability inception and recovery rates is predominantly carried out by combining generalized linear models with time series forecasting techniques into a two-step method involving parameter estimation from historical data and subsequent calibration of a time series model. This approach may lead to both conceptual and numerical problems since any time trend components of the model are incoherently treated as both model parameters and realizations of a stochastic process. We suggest that this general two-step approach can be improved in the following way: First, we assume a stochastic process form for the time trend component. The corresponding transition densities are then incorporated into the likelihood, and the model parameters are estimated using the Expectation-Maximization algorithm. We illustrate the modeling procedure by fitting the model to Swedish disability claims data.

Place, publisher, year, edition, pages
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD, 2018
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-230862 (URN)10.1080/10920277.2017.1387570 (DOI)000433300800006 ()2-s2.0-8503862925 (Scopus ID)
Note

QC 20180618

Available from: 2018-06-18 Created: 2018-06-18 Last updated: 2018-06-25Bibliographically approved
Aurell, A. & Djehiche, B. (2018). Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics. SIAM Journal of Control and Optimization, 56(1), 434-455
Open this publication in new window or tab >>Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics
2018 (English)In: SIAM Journal of Control and Optimization, ISSN 0363-0129, E-ISSN 1095-7138, Vol. 56, no 1, p. 434-455Article in journal (Refereed) Published
Abstract [en]

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications, 2018
Keywords
Crowd aversion, Crowd dynamics, Interacting populations, Mean-field approximation, Mean-field type game, Optimal control
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-224585 (URN)10.1137/17M1119196 (DOI)000426744900020 ()2-s2.0-85043490666 (Scopus ID)
Funder
Swedish Research Council, 2016-04086
Note

QC 20180320

Available from: 2018-03-20 Created: 2018-03-20 Last updated: 2018-03-26Bibliographically approved
Djehiche, B. & Nassar, H. (2017). A functional Hodrick-Prescott filter. Journal of Inverse and Ill-Posed Problems, 25(2), 135-148
Open this publication in new window or tab >>A functional Hodrick-Prescott filter
2017 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 25, no 2, p. 135-148Article in journal (Refereed) Published
Abstract [en]

We propose a functional version of the Hodrick-Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH, 2017
Keywords
Inverse problems, adaptive estimation, Hodrick-Prescott filter, smoothing, signal extraction, Gaussian measures on a Hilbert space
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-206696 (URN)10.1515/jiip-2015-0111 (DOI)000398963900001 ()2-s2.0-85016837758 (Scopus ID)
Note

QC 20170509

Available from: 2017-05-09 Created: 2017-05-09 Last updated: 2017-05-09Bibliographically approved
Djehiche, B., Tcheukam, A. & Tembine, H. (2017). A Mean-Field Game of Evacuation in Multilevel Building. IEEE Transactions on Automatic Control, 62(10), 5154-5169
Open this publication in new window or tab >>A Mean-Field Game of Evacuation in Multilevel Building
2017 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 62, no 10, p. 5154-5169Article in journal (Refereed) Published
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-216623 (URN)10.1109/TAC.2017.2679487 (DOI)000412429600018 ()2-s2.0-85031011176 (Scopus ID)
Note

QC 20171102

Available from: 2017-11-02 Created: 2017-11-02 Last updated: 2018-02-26Bibliographically approved
Djehiche, B., Hamadene, S., Morlais, M.-A. & Zhao, X. (2017). On the equality of solutions of max-min and min-max systems of variational inequalities with interconnected bilateral obstacles. Journal of Mathematical Analysis and Applications, 452(1), 148-175
Open this publication in new window or tab >>On the equality of solutions of max-min and min-max systems of variational inequalities with interconnected bilateral obstacles
2017 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 1, p. 148-175Article in journal (Refereed) Published
Abstract [en]

In this paper, we deal with the solutions of systems of PDEs with bilateral interconnected obstacles of min-max and max-min types. These systems arise naturally in stochastic switch-in zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Then, this common viscosity solution is related to a multi-dimensional doubly reflected BSDE with bilateral interconnected obstacles. Finally, its relationship with the values of a zero-sum switching game is studied.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017
Keywords
Switching zero-sum game, PDEs with obstacles, Reflected backward stochastic differential equation, Hamilton-Jacobi-Bellman-Isaacs equation
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-206227 (URN)10.1016/j.jmaa.2017.02.025 (DOI)000398645800009 ()
Note

QC 20170517

Available from: 2017-05-17 Created: 2017-05-17 Last updated: 2017-05-19Bibliographically approved
Bensoussan, A., Djehiche, B., Tembine, H. & Yam, P. (2017). Risk-Sensitive Mean-Field-Type Control. In: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC): . Paper presented at IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA. IEEE
Open this publication in new window or tab >>Risk-Sensitive Mean-Field-Type Control
2017 (English)In: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2017Conference paper, Published paper (Refereed)
Abstract [en]

We study risk-sensitive optimal control of a stochastic differential equation (SDE) of mean-field type, where the coefficients are allowed to depend on some functional of the law as well as the state and control processes. Moreover the risk-sensitive cost functional is also of mean-field type. We derive optimality equations in infinite dimensions connecting dual functions associated with Bellman functional to the adjoint process of the Pontryagin maximum principle. The case of linear-exponentiated quadratic cost and its connection with the risk-neutral solution is discussed.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223843 (URN)10.1109/CDC.2017.8263639 (DOI)000424696900006 ()2-s2.0-85046143547 (Scopus ID)978-1-5090-2873-3 (ISBN)
Conference
IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA
Funder
Swedish Research Council
Note

QC 20180306

Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-11-13Bibliographically approved
Djehiche, B. & Huang, M. (2016). A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type. Dynamic Games and Applications, 6(1), 55-81
Open this publication in new window or tab >>A Characterization of Sub-game Perfect Equilibria for SDEs of Mean-Field Type
2016 (English)In: Dynamic Games and Applications, ISSN 2153-0785, E-ISSN 2153-0793, Vol. 6, no 1, p. 55-81Article in journal (Refereed) Published
Abstract [en]

We study a class of dynamic decision problems of mean-field type with time-inconsistent cost functionals and derive a stochastic maximum principle to characterize sub-game perfect equilibrium points. Subsequently, this approach is extended to a mean-field game to construct decentralized strategies and obtain an estimate of their performance.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Time-inconsistent stochastic control, Maximum principle, Mean-field SDE, Equilibrium, Mean-field game
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-183184 (URN)10.1007/s13235-015-0140-8 (DOI)000369297700003 ()2-s2.0-84957566168 (Scopus ID)
Note

QC 20160303

Available from: 2016-03-03 Created: 2016-03-03 Last updated: 2017-11-30Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-6608-0715

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