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Numerical method for optimal stopping of piecewise deterministic Markov processes

hal.structure.identifierGroupe de Recherche en Economie Théorique et Appliquée [GREThA]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDE SAPORTA, Benoîte
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorDUFOUR, François
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierQuality control and dynamic reliability [CQFD]
dc.contributor.authorGONZALEZ, Karen
dc.date.accessioned2024-04-04T02:35:34Z
dc.date.available2024-04-04T02:35:34Z
dc.date.conference2009-06
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190651
dc.description.abstractEnThe aim of this paper is to propose a computational method for optimal stopping of a piecewise deterministic Markov process by using a quantization technique for an underlying discrete-time Markov chain related to the continuous-time process and path-adapted time discretization grids. Piecewise-deterministic Markov processes (PDMP's) have been introduced in the literature by M.H.A. Davis \cite{davis93} as a general class of stochastic models covering a great number of problems of operations research. PDMP's are a family of Markov processes involving deterministic motion punctuated by random jumps. It was shown in \cite{gugerli86} that the value function of the optimal stopping problem can be calculated by iterating a functional operator which involves a continuous-time maximization and a discrete-time dynamic programming formula. To approximate the value function of the optimal stopping problem of a PDMP, a natural approach would have been to follow the same lines as in \cite{bally03} for diffusion processes, unfortunately their method cannot be directly applied here. However, by using the special structure of PDMP's, we are able to propose an approximation scheme for the value function and derive a rate of convergence. In addition and more importantly, this numerical approximation scheme enables us to propose, without any additional calculations, a computable stopping rule which also is an $\epsilon$-optimal stopping time of the original problem, and we can characterize how far it is from optimal in terms of the value function.
dc.language.isoen
dc.title.enNumerical method for optimal stopping of piecewise deterministic Markov processes
dc.typeCommunication dans un congrès
dc.subject.halMathématiques [math]/Probabilités [math.PR]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.conference.titleOPTIMAL STOPPING WITH APPLICATIONS
bordeaux.countryFI
bordeaux.conference.cityTurku
bordeaux.peerReviewedoui
hal.identifierhal-00400183
hal.version1
hal.invitednon
hal.proceedingsnon
hal.popularnon
hal.audienceNon spécifiée
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00400183v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=DE%20SAPORTA,%20Beno%C3%AEte&DUFOUR,%20Fran%C3%A7ois&GONZALEZ,%20Karen&rft.genre=unknown


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