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On approximative solutions of optimal stopping problems

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  01 July 2016

Andreas Faller  and
Ludger Rüschendorf
Andreas Faller*
Affiliation:
University of Freiburg
Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
∗ Andreas Faller died unexpectedly on 30 June 2011.
∗∗ Postal address: Mathematical Stochastics, University of Freiburg, Eckerstr. 1, 79104 Freiburg, Germany. Email address: ruschen@stochastik.uni-freiburg.de
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Abstract

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In this paper we establish an extension of the method of approximating optimal discrete-time stopping problems by related limiting stopping problems for Poisson-type processes. This extension allows us to apply this method to a larger class of examples, such as those arising, for example, from point process convergence results in extreme value theory. Furthermore, we develop new classes of solutions of the differential equations which characterize optimal threshold functions. As a particular application, we give a fairly complete discussion of the approximative optimal stopping behavior of independent and identically distributed sequences with discount and observation costs.

Keywords

Optimal stoppingmax-stable distributionPoisson process

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 62L15: Optimal stopping
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1086 - 1108
Copyright
Copyright © Applied Probability Trust 2011 

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