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The disorder problem for compound Poisson processes with exponential jumps

Pavel V. Gapeev
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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 Levy 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.

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Pavel V. Gapeev. 2005-03-23. The disorder problem for compound Poisson processes with exponential jumps. https://doi.org/10.1214/105051604000000981

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