A claims persistence process and insurance

Pierre Vallois, Charles Tapiero

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)367-373
Number of pages7
JournalInsurance Mathematics and Economics
Volume44
Issue number3
DOIs
StatePublished - Jun 2009

Fingerprint

Insurance
Persistence
Calculate
Probability generating function
Period of time
Generating Function
Counting
Random walk
Markov chain
Probability Distribution
Generating function
Moment
Dependent

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

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

In: Insurance Mathematics and Economics, Vol. 44, No. 3, 06.2009, p. 367-373.

Research output: Contribution to journalArticle

@article{a29c797a991c48f9997d4fb3a8ad2175,
title = "A claims persistence process and insurance",
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).",
keywords = "Insurance claims, Persistence, Random walk, Value at risk",
author = "Pierre Vallois and Charles Tapiero",
year = "2009",
month = "6",
doi = "10.1016/j.insmatheco.2008.11.009",
language = "English (US)",
volume = "44",
pages = "367--373",
journal = "Insurance: Mathematics and Economics",
issn = "0167-6687",
publisher = "Elsevier",
number = "3",

}

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

VL - 44

SP - 367

EP - 373

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

SN - 0167-6687

IS - 3

ER -