We consider a model for the risk reserve Z (t) of an insurance company.
It is assumed that Z (t) increases due to premium intake and also as the reserve earns interest.
The reserve decreases due to claims, which are modeled as a compound Poisson process.
Previously [SIAM J. Appl.
Math., 54 (1994), pp. 1745-1767 we obtained an integral representation for the probability that Z (t) remains positive through time t, which is also the probability that the company survives up to this time.
We now study asymptotic properties of this probability.
It is assumed that the rate at which the reserve earns interest is small (but nonzero).
Mots-clés Pascal : Application, Evaluation risque, Probabilité, Stabilité, Equation intégrodifférentielle, Processus aléatoire, Modèle mathématique, Théorie
Mots-clés Pascal anglais : Risk reserve, Insurance company, Poisson process, Integral representation, Collective rain, Asymptotic properties, Application, Risk assessment, Probability, Stability, Integrodifferential equations, Random processes, Mathematical models, Theory
Notice produite par :
Inist-CNRS - Institut de l'Information Scientifique et Technique
Cote : 96-0467661
Code Inist : 001A02I01. Création : 10/04/1997.