Optimal time to change premiums

Erhan Bayraktar, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)125-158
Number of pages34
JournalMathematical Methods of Operations Research
Volume68
Issue number1
DOIs
StatePublished - Aug 2008

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)
  • Management Science and Operations Research

Keywords

  • Compound Poisson processes
  • Detecting the change in the characteristics of the claim arrival process
  • Insurance premiums
  • Optimal stopping

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