Effective Statistical Learning Methods for Actuaries I: GLMs and Extensions

✍ Scribed by Michel Denuit, Donatien Hainaut, Julien Trufin

Publisher: Springer International Publishing
Year: 2019
Tongue: English
Leaves: 452
Series: Springer Actuarial
Edition: 1st ed. 2019
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book summarizes the state of the art in generalized linear models (GLMs) and their various extensions: GAMs, mixed models and credibility, and some nonlinear variants (GNMs). In order to deal with tail events, analytical tools from Extreme Value Theory are presented. Going beyond mean modeling, it considers volatility modeling (double GLMs) and the general modeling of location, scale and shape parameters (GAMLSS). Actuaries need these advanced analytical tools to turn the massive data sets now at their disposal into opportunities.

The exposition alternates between methodological aspects and case studies, providing numerical illustrations using the R statistical software. The technical prerequisites are kept at a reasonable level in order to reach a broad readership.

This is the first of three volumes entitled Effective Statistical Learning Methods for Actuaries. Written by actuaries for actuaries, this series offers a comprehensive overview of insurance data analytics with applications to P&C, life and health insurance. Although closely related to the other two volumes, this volume can be read independently.

✦ Table of Contents

Front Matter ....Pages i-xvi
Front Matter ....Pages 1-1
Insurance Risk Classification (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 3-26
Exponential Dispersion (ED) Distributions (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 27-68
Maximum Likelihood Estimation (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 69-94
Front Matter ....Pages 95-95
Generalized Linear Models (GLMs) (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 97-196
Over-Dispersion, Credibility Adjustments, Mixed Models, and Regularization (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 197-250
Front Matter ....Pages 251-251
Generalized Additive Models (GAMs) (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 253-327
Beyond Mean Modeling: Double GLMs and GAMs for Location, Scale and Shape (GAMLSS) (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 329-359
Front Matter ....Pages 361-361
Some Generalized Non-linear Models (GNMs) (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 363-400
Extreme Value Models (Michel Denuit, Donatien Hainaut, Julien Trufin)....Pages 401-441

✦ Subjects

Mathematics; Actuarial Sciences; Statistics for Business/Economics/Mathematical Finance/Insurance

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