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On Threshold Strategies and the Smooth-Fit Principle for Optimal Stopping Problems

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Stéphane Villeneuve
Stéphane Villeneuve*
Affiliation:
Université de Toulouse 1
*
∗ Postal address: Manufacture des Tabacs, Université de Toulouse 1, 21 Allée de Brienne, 31000 Toulouse, France. Email address: stephane.villeneuve@univ-tlse1.fr
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Abstract

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In this paper we investigate sufficient conditions that ensure the optimality of threshold strategies for optimal stopping problems with finite or perpetual maturities. Our result is based on a local-time argument that enables us to give an alternative proof of the smooth-fit principle. Moreover, we present a class of optimal stopping problems for which the propagation of convexity fails.

Keywords

Optimal stoppingprinciple of smooth fitlocal time

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 60J60: Diffusion processes
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007 , pp. 181 - 198
Copyright
Copyright © Applied Probability Trust 2007 

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