Optimal stopping problems for some Markov processes

Mamadou Cissé; Pierre Patie; Etienne Tanré

inria-00458901, version 4

Optimal stopping problems for some Markov processes

Mamadou Cissé ()^a^, 1, Pierre Patie ()^b^, 2, Etienne Tanré () ³

Annals of Applied Probability 22, 3 (2012) 1243-1265

Résumé : In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results to the class of one-sided regular Feller processes. This generalizes the result of Beibel and Lerche [Statist. Sinica 7 (1997) 93-108] and [Teor. Veroyatn. Primen. 45 (2000) 657-669] and Irles and Paulsen [Sequential Anal. 23 (2004) 297-316]. Our approach relies on a combination of techniques borrowed from potential theory and stochastic calculus. We illustrate our results by detailing some new examples ranging from linear diffusions to Markov processes of the spectrally negative type.

a – ENSAE - Sénégal
b – Université Libre de Bruxelles
1 : Ecole Nationale de la Statistique et de l'Analyse Economique (ENSAE)
Ecole Nationale de la Statistique et de l'Analyse Economique
2 : Université Libre de Bruxelles (ULB)
Université Libre de Bruxelles
3 : TOSCA (INRIA Sophia Antipolis / INRIA Nancy - Grand Est/ IECN)
INRIA – CNRS : UMR7502 – Université de Lorraine

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Contributeur : Etienne Tanré <>
Soumis le : Lundi 5 Novembre 2012, 15:16:13
Dernière modification le : Mardi 13 Novembre 2012, 15:20:23

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arXiv : 1106.3158

DOI : 10.1214/11-AAP795

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