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New Perspectives and Methods in Loss Reserving Using Generalized Linear Models

Title:

New Perspectives and Methods in Loss Reserving Using Generalized Linear Models

Tao, Jian (2014) New Perspectives and Methods in Loss Reserving Using Generalized Linear Models. Masters thesis, Concordia University.

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Abstract

Loss reserving has been one of the most challenging tasks that actuaries face since the appearance of insurance contracts. The most popular statistical methods in the loss reserving literature are the Chain Ladder Method and the Bornhuetter Ferguson Method.

Recently, Generalized Linear Models (GLMs) have been used increasingly in insurance model fitting. Some
aggregate loss reserving models have been developed within the framework of GLMs (especially Tweedie distributions). In this thesis we look at loss reserving from the perspective of individual risk classes. A structural loss reserving model is built which combines the exposure, the loss emergence pattern and the loss development pattern together, again within the framework of GLMs. Incurred but not reported (IBNR) losses and Reported but not settled (RBNS) losses are forecasted separately. Finally, we use out of sample tests to show that our method is superior to the traditional methods.

In the third chapter we also extend the theory of limited fluctuation credibility for GLMs to one for GLMMs. Some criteria and algorithms are given. This is a byproduct of our work but is interesting in its own sake. The asymptotic variance of the estimators is derived, both for the marginal mean and the cluster specific mean.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Tao, Jian
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:September 2014
Thesis Supervisor(s):Garrido, Jose
ID Code:978937
Deposited By: JIAN TAO
Deposited On:11 Nov 2014 17:30
Last Modified:18 Jan 2018 17:48
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