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Corrected random walk approximations to free boundary problems in optimal stopping

Part of: Stochastic processes Stochastic analysis

Published online by Cambridge University Press:  01 July 2016

Tze Leung Lai ,
Yi-Ching Yao  and
Farid Aitsahlia
Tze Leung Lai*
Affiliation:
Stanford University
Yi-Ching Yao*
Affiliation:
Academia Sinica
Farid Aitsahlia*
Affiliation:
University of Florida
*
∗ Postal address: Department of Statistics, Stanford University, Stanford, CA 94305, USA. Email address: lait@stat.stanford.edu
∗∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan, ROC. Email address: yao@stat.sinica.edu.tw
∗∗∗ Postal address: Department of Industrial and Systems Engineering, University of Florida, PO Box 116595, Gainesville, FL 32611-6595, USA. Email address: farid@ise.ufl.edu
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Abstract

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Corrected random walk approximations to continuous-time optimal stopping boundaries for Brownian motion, first introduced by Chernoff and Petkau, have provided powerful computational tools in option pricing and sequential analysis. This paper develops the theory of these second-order approximations and describes some new applications.

Keywords

Optimal stoppingfree boundary partial differential equationrandom walkrenewal theorysingular stochastic control

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 90C39: Dynamic programming
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 39 , Issue 3 , September 2007 , pp. 753 - 775
Copyright
Copyright © Applied Probability Trust 2007 

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