Prediction of outstanding liabilities is an important problem in non-life insurance. In the framework of the Solvency II Project, the best estimate must be derived by well defined probabilistic models properly calibrated on the relevant claims experience. A general model along these lines was proposed earlier by Norberg (1993, 1999), who suggested modelling claim arrivals and payment streams as a marked point process. In this paper we specify that claims occur in [0,1] according to a Poisson point process, possibly non-homogeneous, and that each claim initiates a stream of payments, which is modelled by a non-homogeneous compound Poisson process. Consecutive payment streams are i.i.d. and independent of claim arrivals. We find estimates for the total payment in an interval (v,v+s], where v≥1, based upon the total payment up to time v. An estimate for Incurred But Not Reported (IBNR) losses is also given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am41-4-1,
author = {T. Rolski and A. Tomanek},
title = {A continuous-time model for claims reserving},
journal = {Applicationes Mathematicae},
volume = {41},
year = {2014},
pages = {277-300},
zbl = {1309.91077},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-4-1}
}
T. Rolski; A. Tomanek. A continuous-time model for claims reserving. Applicationes Mathematicae, Tome 41 (2014) pp. 277-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-4-1/