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The disorder problem for compound Poisson processes with exponential jumps

Gapeev, Pavel V. (2005) The disorder problem for compound Poisson processes with exponential jumps. Annals of Applied Probability, 15 (1A). pp. 487-499. ISSN 1050-5164

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Identification Number: 10.1214/105051604000000981


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.

Item Type: Article
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Additional Information: © 2005 Institute of Mathematical Statistics
Divisions: Mathematics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 29 Jan 2008
Last Modified: 20 Sep 2021 00:45

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