Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-24T06:27:20.278Z Has data issue: false hasContentIssue false
  • English
  • Français

Claims Reserving Using Tweedie's Compound Poisson Model

Published online by Cambridge University Press:  17 April 2015

Mario V. Wüthrich
Mario V. Wüthrich*
Affiliation:
Winterthur Insurance, Römerstrasse 17, P.O. Box 357, CH-8401 Winterthur, Switzerland, E-mail: mario.wuethrich@winterthur.ch
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the problem of claims reserving and estimating run-off triangles. We generalize the gamma cell distributions model which leads to Tweedie's compound Poisson model. Choosing a suitable parametrization, we estimate the parameters of our model within the framework of generalized linear models (see Jørgensen-de Souza [2] and Smyth-Jørgensen [8]). We show that these methods lead to reasonable estimates of the outstanding loss liabilities.

Keywords

Claims ReservingRun-off TrianglesIBNRCompound Poisson ModelExponential FamilyGLMMSEP
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 33 , Issue 2 , November 2003 , pp. 331 - 346
Copyright
Copyright © ASTIN Bulletin 2003

References

England, P.D., and Verrall, R.J. (2002) Stochastic claims reserving in general insurance, Institute of Actuaries and Faculty of Actuaries, http://www.actuaries.org.uk/files/pdf/sessional/sm0201.pdf Google Scholar
Jørgensen, B., and De Souza, M.C.P. (1994) Fitting Tweedie's compound Poisson model to insurance claims data, Scand. Actuarial J., 69–93.CrossRefGoogle Scholar
Mack, T. (1991) A simple parametric model for rating automobile insurance or estimating IBNR claims reserves, Astin Bulletin 21, 93–109.CrossRefGoogle Scholar
Mack, T. (1997) Measuring the variability of chain ladder reserve estimates, Claims Reserving Manual 2, D6.1–D6.65.Google Scholar
McCullagh, P., and Nelder, J.A. (1989) Generalized linear models, 2nd edition, Chapman and Hall.Google Scholar
Renshaw, A.E., and Verrall, R.J. (1998) A stochastic model underlying the chain-ladder technique, B.A.J. 4, 903–923.Google Scholar
Smyth, G.K. (1996) Partitioned algorithms for maximum likelihood and other nonlinear estimation, Statistics and Computing 6, 201–216.CrossRefGoogle Scholar
Smyth, G.K., and Jørgensen, B. (2002), Fitting Tweedie's compound Poisson model to insurance claims data: dispersion modelling, Astin Bulletin 32, 143–157.CrossRefGoogle Scholar
Taylor, G. (2000), Loss reserving: an actuarial perspective, Kluwer Academic Publishers.CrossRefGoogle Scholar
Tweedie, M.C.K. (1984), An index which distinguishes between some important exponential families. In Statistics: Applications and new directions. Proceeding of the Indian Statistical Golden Jubilee International Conference, Eds. Ghosh, J.K. and Roy, J., 579–604, Indian Statistical Institute, Calcutta.Google Scholar
Wright, T.S. (1990), A stochastic method for claims reserving in general insurance, J.I.A. 117, 677–731.Google Scholar