Open Access
June 2012 Optimal stopping problems for some Markov processes
Mamadou Cissé, Pierre Patie, Etienne Tanré
Ann. Appl. Probab. 22(3): 1243-1265 (June 2012). DOI: 10.1214/11-AAP795


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.


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Mamadou Cissé. Pierre Patie. Etienne Tanré. "Optimal stopping problems for some Markov processes." Ann. Appl. Probab. 22 (3) 1243 - 1265, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1246.60065
MathSciNet: MR2977991
Digital Object Identifier: 10.1214/11-AAP795

Primary: 60G40
Secondary: 60J60 , 60J75

Keywords: Doob’s h-transform , excessive functions , Feller processes , Optimal stopping problems

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
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