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Optimal Time to Change Premiums

Erhan Bayraktar·H. Vincent Poor
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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.

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Erhan Bayraktar, H. Vincent Poor. 2007-03-28. Optimal Time to Change Premiums. https://arxiv.org/abs/math/0703828

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