The disorder problem for compound Poisson processes with exponential jumps

Details The disorder problem for compound Poisson processes with exponential jumps The disorder problem for compound Poisson processes with exponential jumps

2005-03-23

arxiv.org/abs/math/0503481v1

Annals of Applied Probability 2005, Vol. 15, No. 1A, 487-499

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000981 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

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 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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