Optimal stopping problems for some Markov processes
Abstract
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.
Cite
@article{arxiv.1106.3158,
title = {Optimal stopping problems for some Markov processes},
author = {Mamadou Cissé and Pierre Patie and Etienne Tanré},
journal= {arXiv preprint arXiv:1106.3158},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP795 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)