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Generalized Linear Models beyond the Exponential Family with Loss Reserve Applications*

Published online by Cambridge University Press:  17 April 2015

Gary G. Venter
Gary G. Venter*
Affiliation:
E-mail: [email protected]
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Abstract

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The formulation of generalized linear models in Klugman, Panjer and Willmot (2004) is a bit more general than is often seen, in that the residuals are not restricted to following a member of the exponential family. Some of the distributions this allows have potentially useful applications. The cost is that there is no longer a single form for the likelihood function, so each has to be fit directly. Here the use of loss distributions (frequency, severity and aggregate) in generalized linear models is addressed, along with a few other possibilities.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 345 - 364
Copyright
Copyright © ASTIN Bulletin 2007

Footnotes

*

An earlier version of this paper was posted to the August 2007 E-Forum of the Casualty Actuarial Society.

References

Clark, D. and Thayer, C. (2004) A Primer on the Exponential Family of Distributions, Casualty Actuarial Society Discussion Paper Program, 117–148.Google Scholar
Fu, L. and Wu, C. (2005) Generalized Minimum Bias Models, CAS Forum , Winter, 73–121.Google Scholar
Hewitt, C. (1966) Distribution by Size of Risk-A Model, PCAS LIII: 106–114.Google Scholar
Kaas, R. (2005) Compound Poisson Distributions And GLM’s — Tweedie’s Distribution, The Royal Flemish Academy of Belgium for Science and the Arts, http://www.kuleuven.be/ucs/seminars_events/other/files/3afmd/Kaas.PDF Google Scholar
Klugman, S., Panjer, H. and Willmot, G. (2004) Loss Models: From Data to Decisions, 2nd Edition, Wiley.Google Scholar
Mack, T. (2002) Schadenversicherungsmathematik, 2nd Edition, Verlag Versicherungswirtshaft, Karlsruhe, Germany Google Scholar
Mildenhall, S. (1999) A Systematic Relationship between Minimum Bias and Generalized Linear Models, PCAS LXXVI: 393–487.Google Scholar
Mildenhall, S. (2005) Discussion of Generalized Minimum Bias Models, CAS Forum , Winter, 122–124.Google Scholar
Mong, S. (1980) Estimating Aggregate Loss Probability and Increased Limit Factor, Casualty Actuarial Society Discussion Paper Program, 358–393.Google Scholar
Renshaw, A. (1994) Modeling the Claims Process in the Presence of Covariates, ASTIN Bulletin 24(2), 265–286.CrossRefGoogle Scholar
Taylor, G. and Ashe, F. (1983) Second Moments of Estimates of Outstanding Claims. Journal of Econometrics 23, 37–61.CrossRefGoogle Scholar
Venter, G. (2007) Refining Reserve Runoff Ranges, ASTIN Colloquium and CAS E-Forum, August.Google Scholar