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A continuous-time model for claims reserving

Volume 41 / 2014

T. Rolski, A. Tomanek Applicationes Mathematicae 41 (2014), 277-300 MSC: Primary 91B30; Secondary 60K30, 60G55. DOI: 10.4064/am41-4-1

Abstract

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.

Authors

  • T. RolskiMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • A. TomanekMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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