Poisson disorder problem with exponential penalty for delay
成果类型：
Article
署名作者：
Bayraktar, Erhan; Dayanik, Savas
署名单位：
University of Michigan System; University of Michigan; Princeton University
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.1060.0190
发表日期：
2006
页码：
217-233
关键词：
摘要：
We solve the Poisson disorder problem when the delay is penalized exponentially. Our objective is to detect as quickly as possible the unobservable time of the change (or disorder) in the intensity of a Poisson process. The disorder time delimits two different regimes in which one employs distinct strategies (e.g., investment, advertising, manufacturing). We seek a stopping rule that minimizes the frequency of false alarms and an exponential (unlike previous formulations, which use a linear) cost function of the detection delay. In the financial applications, the exponential penalty is a more apt measure for the delay cost because of the compounding of the investment growth. The Poisson disorder problem with a linear delay cost was studied by Peskir and Shiryaev [2002. Solving the Poisson Disorder Problem. Advances in Finance and Stochastics. Springer, Berlin, Germany, 295-312], which is a limiting case of ours.
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