The disorder problem for compound Poisson processes with exponential jumps

Pavel V. Gapeev

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of “disorder” when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Lévy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jumps. The method of proof is based on reducing the Bayesian problem to an integro-differential free-boundary problem where, in some cases, the smooth-fit principle breaks down and is replaced by the principle of continuous fit.

Keywords: disorder (quickest detection) problem; Lévy process; compound Poisson process; optimal stopping; integro-differential free-boundary problem; principles of smooth and continuous fit; measure of jumps and its compensator; Girsanov’s theorem for semimartingales; Itô’s formula (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (13)

Published in Annals of Applied Probability, 2005, 15(1A), pp. 487-499. ISSN: 1050-5164

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