Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-27T08:47:06.066Z Has data issue: false hasContentIssue false
  • English
  • Français

COHERENT INCURRED PAID (CIP) MODELS FOR CLAIMS RESERVING

Published online by Cambridge University Press:  18 December 2017

Gilles Dupin ,
Emmanuel Koenig ,
Pierre Le Moine ,
Alain Monfort  and
Eric Ratiarison
Gilles Dupin
Affiliation:
Groupe MONCEAU, Paris, E-Mail: [email protected]
Emmanuel Koenig
Affiliation:
Groupe MONCEAU, Paris, E-Mail: [email protected]
Pierre Le Moine
Affiliation:
Groupe MONCEAU, Paris, E-Mail: [email protected]
Alain Monfort*
Affiliation:
CRESTParis
Eric Ratiarison
Affiliation:
Groupe MONCEAU, Paris, E-Mail: [email protected]
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we first propose a statistical model, called the Coherent Incurred Paid model, to predict future claims, using simultaneously the information contained in incurred and paid claims. This model does not assume log-normality of the levels (or normality of the growth rates) and is semi-parametric since it only specifies the first and the second moments; however, in order to evaluate the impact of the normality assumption, we also propose a benchmark Gaussian version of our model. Correlations between growth rates of incurred and paid claims are allowed and the tail development period is estimated. We also provide methods for computing the Claim Development Results and their Values at Risk in the semi-parametric framework. Moreover, we show how to take into account the updating of the estimation in the computation of the Claim Development Results. An application highlights the practical importance of relaxing the normality assumption and of updating the estimation of the parameters.

Keywords

Incurred and paid claimssimultaneous estimationcorrelationsemi-parametric approachtail developmentpredictionupdatingCDRVaR
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 48 , Issue 2 , May 2018 , pp. 749 - 777
Copyright
Copyright © Astin Bulletin 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boor, J. (2006) Estimating tail development factors: What to do when the triangle runs out. CAS Forum Winter, 345–390.Google Scholar
Choirat, C. and Seri, R. (2012) Discrete parameter models. Statistical Science, 27, 278–293.Google Scholar
Dahms, R. (2008) A loss reserving methods for incomplete data. Bulletin Swiss Association of Actuaries, 1&2, 127–148.Google Scholar
Dahms, R., Merz, M. and Wüthrich, M. (2009) Claims development result for combined claims incurred and claims paid data. Bulletin Français d'Actuariat, 9 (18), 5–39.Google Scholar
Gourieroux, C. and Monfort, A. (1996) Statistics and Econometric Models, vol. 2. New York: Cambridge University Press.Google Scholar
Gourieroux, C., Monfort, A. and Trognon, . (1984) Pseudo maximum likelihood methods: Theory. Econometrica, 52, 680–700.Google Scholar
Halliwell, L.J. (1997) Conjoint prediction of paid and incurred losses. CAS Forum, 241–379.Google Scholar
Halliwell, L.J. (2009) Modeling paid and incurred losses together. CAS Forum, 1–50.Google Scholar
Happ, S., Merz, M. and Wüthrich, M.V. (2012) Claims development result in the paid incurred claim reserving method. Insurance, Mathematics and Economics, 51 (1), 66–72.Google Scholar
Happ, S. and Wüthrich, M.V. (2013) Paid-incurred chain reserving with dependence modelling. ASTIN Bulletin, 43 (1), 1–20.Google Scholar
Koenig, E., Le Moine, P., Monfort, A. and Ratiarison, E. (2015) Evaluating reserve risk in a regulatory perspective. Journal of Insurance Issues, 38 (2), 151–183.Google Scholar
Lancaster, T. (2000) The incidental parameter problem since 1978. Journal of Econometrics, 95, 391–413.CrossRefGoogle Scholar
Liu, H. and Verrall, R. (2010) Bootstrap estimation of the predictive distributions of reserves using paid and incurred claims. Variance, 4 (2), 121–135.Google Scholar
Merz, M. and Wüthrich, M.V. (2010) Paid-Incurred chain claims reserving method. Insurance Mathematics and Economics, 46, 568–579.Google Scholar
Merz, M. and Wüthrich, M.V. (2013) Estimation of tail development factors in the Paid-Incurred chain reserving method. Variance, 7 (1), 61–73.Google Scholar
Moreira, M. (2009) A maximum likelihood method for the incidental parameter problem. The Annals of Statistics, 37, 3660–3696.Google Scholar
Neyman, J. and Scott, E.L. (1948) Consistent estimates based on partially consistent observations. Econometrica, 59, 347–378.Google Scholar
Peters, G., Dong, A. and Kohn, R. (2014) A copula based Bayesian approach for paid-incurred claims models for non-life insurance reserving. Insurance Mathematics and Economics, 30 (59), 258–278.CrossRefGoogle Scholar
Peters, G., Wüthrich, M. and Shevchenko, P. (2010) Chain ladder method: Bayesian bootstrap versus classical bootstrap. Insurance Mathematics and Economics, 47, 36–51.CrossRefGoogle Scholar
Pigeon, M., Antonio, K. and Denuit, M. (2014) Individual loss reserving using paid-incurred data. Insurance Mathematics and Economics, 58, 121–131.CrossRefGoogle Scholar
Posthuma, B., Cator, E.A., Veerkamp, W. and Van Zwet, E.W. (2008) Combined analysis of paid and incurred losses. Casualty Actuarial Society E-Forum, 272–293.Google Scholar
Quarg, C. and Mack, T. (2004) Munich chain ladder. Blatter DGVFM Band, XXVI, 597–630.CrossRefGoogle Scholar
Venter, G.G. (2008) Distribution and value of reserves using paid and incurred triangle. CAS Forum Fall.Google Scholar
Wüthrich, M.V. and Merz, M. (2013) Financial Modeling, Actuarial Valuation and Solvency in Insurance. Berlin, Heidelberg: Springer.Google Scholar