A continuous-time model for claims reserving

T. Rolski¹ ; A. Tomanek¹

¹ Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Applicationes Mathematicae, Tome 41 (2014) no. 4, pp. 277-300.

Résumé

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 $v\ge 1$, based upon the total payment up to time $v$. An estimate for Incurred But Not Reported (IBNR) losses is also given.

Détail

DOI : 10.4064/am41-4-1

Keywords: prediction outstanding liabilities important problem non life insurance framework solvency project best estimate derived defined probabilistic models properly calibrated relevant claims experience general model along these lines proposed earlier norberg who suggested modelling claim arrivals payment streams marked point process paper specify claims occur according poisson point process possibly non homogeneous each claim initiates stream payments which modelled non homogeneous compound poisson process consecutive payment streams independent claim arrivals estimates total payment interval where based total payment time estimate incurred reported ibnr losses given