The disorder problem for compound Poisson processes with exponential jumps
成果类型：
Article
署名作者：
Gapeev, PV
署名单位：
Russian Academy of Sciences; V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/105051604000000981
发表日期：
2005
页码：
487-499
关键词：
摘要：
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.