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Optimal stopping with discount and observation costs

Part of: Stochastic processes Sequential methods

Published online by Cambridge University Press:  14 July 2016

Robert Kühne  and
Ludger Rüschendorf
Robert Kühne*
Affiliation:
University of Freiburg
Ludger Rüschendorf*
Affiliation:
University of Freiburg
*
∗Postal address: Institut für Mathematische Stochastik, Universität Freiburg, Eckerstr. 1, D-79104 Freiburg, Germany
∗Postal address: Institut für Mathematische Stochastik, Universität Freiburg, Eckerstr. 1, D-79104 Freiburg, Germany
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Abstract

For i.i.d. random variables in the domain of attraction of a max-stable distribution with discount and observation costs we determine asymptotic approximations of the optimal stopping values and asymptotically optimal stopping times. The results are based on Poisson approximation of related embedded planar point processes. The optimal stopping problem for the limiting Poisson point processes can be reduced to differential equations for the boundaries. In several cases we obtain numerical solutions of the differential equations. In some cases the analysis allows us to obtain explicit optimal stopping values. This approach thus leads to approximate solutions of the optimal stopping problem of discrete time sequences.

Keywords

Optimal stoppingmax-stable distributionsPoisson processes

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory 62L15: Optimal stopping
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 64 - 72
Copyright
Copyright © 2000 by The Applied Probability Trust 

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