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Beyond the Tweedie reserving model: the collective approach to loss development. (English) Zbl 1414.91178

Summary: This article proposes a new loss reserving approach, inspired from the collective model of risk theory. According to the collective paradigm, we do not relate payments to specific claims or policies, but we work within a frequency-severity setting, with a number of payments in every cell of the run-off triangle, together with the corresponding paid amounts. Compared to the Tweedie reserving model, which can be seen as a compound sum with Poisson-distributed number of terms and Gamma-distributed summands, we allow here for more general severity distributions, typically mixture models combining a light-tailed component with a heavier-tailed one, including inflation effects. The severity model is fitted to individual observations and not to aggregated data displayed in run-off triangles with a single value in every cell. In that respect, the modeling approach appears to be a powerful alternative to both the crude traditional aggregated approach based on triangles and the extremely detailed individual reserving approach developing each and every claim separately. A case study based on a motor third-party liability insurance portfolio observed over 2004–2014 is used to illustrate the relevance of the proposed approach.

MSC:

91B30 Risk theory, insurance (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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References:

[1] Alai, D. H.; Wuthrich, M. V., Taylor Approximations for Model Uncertainty within the Tweedie Exponential Dispersion Family, Astin Bulletin, 39, 453-477, (2009) · Zbl 1180.91158
[2] Boucher, J. P.; Davidov, D., On the Importance of Dispersion Modeling for Claims Reserving: An Application with the Tweedie Distribution, Variance, 5, 158-172, (2011)
[3] Embrechts, P.; Frei, M., Panjer Recursion versus FFT for Compound Distributions, Mathematical Methods of Operations Research, 69, 497-508, (2009) · Zbl 1205.91081
[4] Kaas, R.; Goovaerts, M. J.; Dhaene, J.; Denuit, M., Modern actuarial risk theory using R, (2008), New York: Springer, New York · Zbl 1148.91027
[5] Peters, G. W.; Shevchenko, P. V.; Wuthrich, M. V., Model Uncertainty in Claims Reserving within Tweedie’s Compound Poisson Models, Astin Bulletin, 39, 1-33, (2009) · Zbl 1203.91114
[6] Rosenlund, S., Dispersion Estimates for Poisson and Tweedie Models, Astin Bulletin, 40, 271-279, (2010) · Zbl 1189.62165
[7] Schiegl, M., On the Safety Loading for Chain Ladder Estimates: A Monte Carlo Simulation Study, Astin bulletin, 32, 107-128, (2002) · Zbl 1061.62568
[8] Schiegl, M., A Model Study about the Applicability of the Chain Ladder Method, Scandinavian Actuarial Journal, 2015, 482-499, (2015) · Zbl 1401.91190
[9] Stasinopoulos, M. D.; Rigby, R. A.; Heller, G. Z.; Voudouris, V.; De Bastiani, F., Flexible regression and smoothing: using gamlss in r, (2017), New York: Chapman and Hall/CRC, New York
[10] Wuthrich, M. V., Claims Reserving using Tweedie’s Compound Poisson Model, Astin Bulletin, 33, 331-346, (2003) · Zbl 1095.91042
[11] Wuthrich, M. V.; Merz, M., Stochastic claims reserving methods in insurance, (2008), New York: Wiley, New York · Zbl 1273.91011
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