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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.

MSC:

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

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