Abstract
Generalized Linear Models are widely known under their famous acronym GLMs. Today, GLMs are recognized as an industry standard for pricing personal lines and small commercial lines of insurance business. This chapter reviews the GLM methodology with a special emphasis to insurance problems. The statistical framework of GLMs allows the actuary to make explicit assumptions about the nature of insurance data, claim counts or claim costs for instance, and their relationship with the available features. This makes the analysis transparent and relatively easy to communicate, even to non-specialists.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The full, and official, name of the tables is Actuarial Tables with explanatory notes for use in Personal Injury and Fatal Accident Cases but the unofficial name has now become common parlance, after Sir Michael Ogden having been the chairman of the Working Party for the first four editions.
References
Ajne B (1986) Comparison of some methods to fit a multiplicative tariff structure to observed risk data. ASTIN Bull 16:63–68
Bailey RA (1963) Insurance rates with minimum bias. Proc Casualty Actuar Soc 93:4–11
Charpentier A (2014) Computational actuarial science with R. The R Series. Chapman & Hall/CRC
De Jong P, Heller GZ (2008) Generalized linear models for insurance data. Cambridge University Press
Denuit M, Marechal X, Pitrebois S, Walhin J-F (2007) Actuarial modelling of claim counts: risk classification, credibility and bonus-malus systems. Wiley
Dunn PK, Smyth GK (2019) Generalized linear models with examples in R. Springer, New York
Efron B (1986) How biased is the apparent error rate of a prediction rule? J Am Stat Assoc 81:461–470
Fahrmeir L, Kneib T, Lang S, Marx B (2013) Regression models, methods and applications. Springer
Faraway JJ (2005a) Linear models with R. Chapman & Hall/CRC
Faraway JJ (2005b) Extending the linear model with R. Chapman & Hall/CRC
Fox J (2016a) Applied regression analysis and generalized linear models. Sage Publications
Fox J (2016b) A R companion to applied regression analysis and generalized linear models. Sage Publications
Frees EW, Derrig RA, Meyers G (2014) Predictive modeling applications in actuarial science. Volume I: predictive modeling techniques. International Series on Actuarial Science. Cambridge University Press
Goldburg M, Khare A, Tevet D (2016) Generalized linear models for insurance pricing. CAS Monograph Series, Number 5. http://www.casact.org/
Hainaut D, Trufin J, Denuit M (2019) Effective statistical learning methods for actuaries—neural networks and unsupervised methods. Springer Actuarial Series
Horowitz JL (2009) Semiparametric and nonparametric methods in econometrics. Springer, New York
Jung J (1968) On automobile insurance ratemaking. ASTIN Bull 5:41–48
Kaas R, Goovaerts MJ, Dhaene J, Denuit M (2008) Modern actuarial risk theory using R. Springer, Berlin
Mc Cullagh P, Nelder JA (1989) Generalized linear models. Chapman & Hall, New York
Mildenhall SJ (1999) A systematic relationship between minimum bias and generalized linear models. Proc Casualty Actuar Soc 86:393–487
Nelder JA, Wedderburn RWM (1972) Generalized linear models. J R Stat Soc Ser A 135:370–384
Ohlsson E, Johansson B (2010) Non-life insurance pricing with generalized linear models. Springer, Berlin
Trufin J, Denuit M, Hainaut D (2019) Effective statistical learning methods for actuaries—tree-based methods. Springer Actuarial Series
Wuthrich MV, Buser C (2017) Data analytics for non-life insurance pricing. Swiss Finance Institute Research Paper No. 16–68. SSRN: https://ssrn.com/abstract=2870308
Yan J, Guszcza J, Flynn M, Wu CSP (2009) Applications of the offset in property-casualty predictive modeling. In: Casualty actuarial society e-forum, winter 2009, pp 366–385
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Denuit, M., Hainaut, D., Trufin, J. (2019). Generalized Linear Models (GLMs). In: Effective Statistical Learning Methods for Actuaries I. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-030-25820-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-25820-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-25819-1
Online ISBN: 978-3-030-25820-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)