A Claims Persistence Process and Insurance

Pierre P. Vallois (1, 2) , Charles S. Tapiero (3)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 Department of Finance and Risk Engineering

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).

Mots clés: Random walk; Persistence; Insurance claims; Value at risk

Domaines: Probabilités [math.PR]

Pierre P. Vallois, Charles S. Tapiero. A Claims Persistence Process and Insurance. Insurance: Mathematics and Economics, 2009, 44 (3), pp.367-373. ⟨10.1016/j.insmatheco.2008.11.009⟩. ⟨hal-00591746⟩