The Disorder Problem for Compound Poisson Processes with Exponential Jumps
نویسنده
چکیده
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.
منابع مشابه
THE DISORDER PROBLEM FOR COMPOUND POISSON PROCESSES WITH EXPONENTIAL JUMPS BY PAVEL V. GAPEEV Russian Academy of Sciences
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