Effective Statistical Learning Methods for Actuaries I by Michel Denuit & Donatien Hainaut & Julien Trufin

Author:Michel Denuit & Donatien Hainaut & Julien Trufin
Language: eng
Format: epub
ISBN: 9783030258207
Publisher: Springer International Publishing

On the other hand, it can be corrected so that the model exactly reproduces the total costs at portfolio level for each calendar year (a useful property that is known to hold for the Poisson and overdispersed Poisson models, for instance).

These parameters can then be projected to the future in the pricing.

5.5.2 Modeling Panel Data with Static Random Effects

Responses are now doubly indexed, by policy and by time , where denotes the number of observation periods for contract i. Given , the observations relating to policyholder i are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function together with a dispersion parameter. These observations are gathered in the random vector of dimension . Even if it is often reasonable to assume independence between the random vectors , this assumption is generally questionable inside these vectors because of repeated measures on the same individual.

Formally, the basic GLMMs rely on the two following assumptions: A1

The random vectors are mutually independent and given , the response obeys the ED probability density or probability mass function

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