Optimal time to change premiums

Erhan Bayraktar and H. Poor ()

Mathematical Methods of Operations Research, 2008, vol. 68, issue 1, 125-158

Abstract: The claim arrival process to an insurance company is modeled by a compound Poisson process whose intensity and/or jump size distribution changes at an unobservable time with a known distribution. It is in the insurance company’s interest to detect the change time as soon as possible in order to re-evaluate a new fair value for premiums to keep its profit level the same. This is equivalent to a problem in which the intensity and the jump size change at the same time but the intensity changes to a random variable with a know distribution. This problem becomes an optimal stopping problem for a Markovian sufficient statistic. Here, a special case of this problem is solved, in which the rate of the arrivals moves up to one of two possible values, and the Markovian sufficient statistic is two-dimensional. Copyright Springer-Verlag 2008

Keywords: Compound Poisson processes; Optimal stopping; Detecting the change in the characteristics of the claim arrival process; Insurance premiums (search for similar items in EconPapers)
Date: 2008
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Working Paper: Optimal Time to Change Premiums (2007)
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DOI: 10.1007/s00186-007-0182-9

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