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Author Peskir, G. ♦ Shiryaev, A. N.
Source CiteSeerX
Content type Text
Publisher Springer
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Main Purpose ♦ Smooth Fit Break ♦ Continuous Fit ♦ Optimal Stopping ♦ Key Point ♦ Posteriori Probability Process ♦ Partial Answer ♦ Special Case ♦ Present Paper ♦ Proof Consists ♦ Probabilistic Term ♦ Observed Poisson Process Change ♦ Stopping Time ♦ General Case ♦ Sample Path Behaviour ♦ Analytic Term ♦ Singularity Point ♦ Poisson Disorder Problem ♦ Free-boundary Equation ♦ Freeboundary Differential-difference Problem
Description The Poisson disorder problem seeks to determine a stopping time which is as close as possible to the (unknown) time of ’disorder ’ when the intensity of an observed Poisson process changes from one value to another. Partial answers to this question are known to date only in some special cases, and the main purpose of the present paper is to describe the structure of the solution in the general case. The method of proof consists of reducing the initial (optimal stopping) problem to a freeboundary differential-difference problem. The key point in the solution is reached by specifying when the principle of smooth fit breaks down and gets superseded by the principle of continuous fit. This can be done in probabilistic terms (by describing the sample path behaviour of the a posteriori probability process) and in analytic terms (via the existence of a singularity point of the free-boundary equation). 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 2002-01-01
Publisher Institution Advances in Finance and Stochastics