### Abstract

The purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating function of the number of claims over time and as a result are able to calculate their moments. Further, given the claims severity probability distribution, we provide both the claims process generating function as well as the mean and the claim variance that an insurance firm confronts over a given period of time and in such circumstances. A number of results and applictions are then outlined (such as a Compound Claim Persistence Process).

Original language | English (US) |
---|---|

Pages (from-to) | 367-373 |

Number of pages | 7 |

Journal | Insurance Mathematics and Economics |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2009 |

### Fingerprint

### Keywords

- Insurance claims
- Persistence
- Random walk
- Value at risk

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Economics and Econometrics
- Statistics and Probability

### Cite this

*Insurance Mathematics and Economics*,

*44*(3), 367-373. https://doi.org/10.1016/j.insmatheco.2008.11.009

**A claims persistence process and insurance.** / Vallois, Pierre; Tapiero, Charles.

Research output: Contribution to journal › Article

*Insurance Mathematics and Economics*, vol. 44, no. 3, pp. 367-373. https://doi.org/10.1016/j.insmatheco.2008.11.009

}

TY - JOUR

T1 - A claims persistence process and insurance

AU - Vallois, Pierre

AU - Tapiero, Charles

PY - 2009/6

Y1 - 2009/6

N2 - The purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating function of the number of claims over time and as a result are able to calculate their moments. Further, given the claims severity probability distribution, we provide both the claims process generating function as well as the mean and the claim variance that an insurance firm confronts over a given period of time and in such circumstances. A number of results and applictions are then outlined (such as a Compound Claim Persistence Process).

AB - The purpose of this paper is to introduce and construct a state dependent counting and persistent random walk. Persistence is imbedded in a Markov chain for predicting insured claims based on their current and past period claim. We calculate for such a process, the probability generating function of the number of claims over time and as a result are able to calculate their moments. Further, given the claims severity probability distribution, we provide both the claims process generating function as well as the mean and the claim variance that an insurance firm confronts over a given period of time and in such circumstances. A number of results and applictions are then outlined (such as a Compound Claim Persistence Process).

KW - Insurance claims

KW - Persistence

KW - Random walk

KW - Value at risk

UR - http://www.scopus.com/inward/record.url?scp=65049086423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65049086423&partnerID=8YFLogxK

U2 - 10.1016/j.insmatheco.2008.11.009

DO - 10.1016/j.insmatheco.2008.11.009

M3 - Article

AN - SCOPUS:65049086423

VL - 44

SP - 367

EP - 373

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 3

ER -