The disorder problem for compound Poisson processes with exponential jumps

Gapeev, Pavel V. ORCID: 0000-0002-1346-2074 (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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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.

Item Type:	Article
Official URL:	http://www.imstat.org/aap/
Additional Information:	© 2005 Institute of Mathematical Statistics
Divisions:	Mathematics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	29 Jan 2008
Last Modified:	01 Nov 2024 05:16
URI:	http://eprints.lse.ac.uk/id/eprint/3219

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