Summary |
This book focuses on methods based on GLMs that we have found useful in our actuarial practice, and intend to provide a set of tools that fills needs for a tariff analysis. Successive versions of the text have been the basis for a course in non-life insurance mathematics at Stockholm University since 2001. This course is part of the curriculum set up the Swedish Actuarial Society to meet the European Core Syllabus for actuarial education.
The aim is to present the basic theory of GLMs in a tariff analysis setting, and also to give some useful extensions of standard GLM theory that are not in common use, viz. the incorporation of random effects and the use of smoothing splines. Random effect models can be used to great advantage for handling categorical variables with a large number of possible levels, and there is an interesting connection with the traditional actuarial field of credibility theory that will be developed here. Smoothing splines is a powerful method for modeling the effect of continuous variables; such analyses are often presented under the name generalized additive models (GAMs). While GAMs have been used in biostatistics for several years, they have not yet found their way into the actuarial domain to any large extent.
The text is intended for practicing actuaries and actuarial students with a background in mathematics and mathematical statistics: proofs are included whenever possible without going into asymptotic theory.
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