Taylor approximations for model uncertainty within the Tweedie exponential dispersion family. (English) Zbl 1180.91158

Summary: The use of generalized linear models (GLM) to estimate claims reserves has become a standard method in insurance. Most frequently, the exponential dispersion family (EDF) is used; see e.g. P. D. England and R. J. Verrall [“Stochastic claims reserving in general insurance”. British Act. J. 8, 443–518 (2002)]. We study the so-called Tweedie EDF and test the sensitivity of the claims reserves and their mean square error of predictions (MSEP) over this family. Furthermore, we develop second order Taylor approximations for the claims reserves and the MSEPs for members of the Tweedie family that are difficult to obtain in practice, but are close enough to models for which claims reserves and MSEP estimations are easy to determine. As a result of multiple case studies, we find that claims reserves estimation is relatively insensitive to which distribution is chosen amongst the Tweedie family, in contrast to the MSEP, which varies widely.


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


[1] Stochastic Claims Reserving Methods in Insurance (2008) · Zbl 1273.91011
[2] Generalized Linear Models (1989)
[3] Theory of Point Estimation (1983)
[4] Scand. Actuar. J. pp 69– (1994)
[5] The Theory of Dispersion Models (1997)
[6] J. Roy. Statist. Soc. 49 pp 127– (1987)
[7] DOI: 10.2307/2988543
[8] Giornale dell’Instituto Italiano degli Attuari 68 pp 55– (2005)
[9] DOI: 10.1017/S1357321700003809
[10] A Course in Credibility Theory and its Applications (2005) · Zbl 1108.91001
[11] DOI: 10.1017/S0515036100013490
[12] Biometrika 61 pp 439– (1974)
[13] An index which distinguishes some important exponential families pp 579– (1984)
[14] DOI: 10.2143/AST.32.1.1020 · Zbl 1094.91514
[15] DOI: 10.2143/AST.24.2.2005070
[16] DOI: 10.2143/AST.39.1.2038054 · Zbl 1203.91114
[17] DOI: 10.2307/2344614
[18] DOI: 10.1093/biomet/74.2.221 · Zbl 0621.62078
[19] 1999 Proceedings of the Casualty Actuarial Society 86 pp 393– (1999)
[20] DOI: 10.2143/AST.21.1.2005403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.