Poisson disorder problem with exponential penalty for delay

Poisson disorder problem with exponential penalty for delay

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Article ID: iaor200934348
Country: United States
Volume: 31
Issue: 2
Start Page Number: 217
End Page Number: 233
Publication Date: May 2006
Journal: Mathematics of Operations Research
Authors: ,
Abstract:

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), which is a limiting case of ours.

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