Electronic Thesis and Dissertation Repository

Thesis Format

Integrated Article

Degree

Master of Science

Program

Statistics and Actuarial Sciences

Supervisor

Jiandong Ren

Abstract

In the thesis, we introduce a two-dimensional semi-linear credibility model, which is an extension of the classical credibility or split credibility models used by practicing actuaries. Our model predicts the future expected losses of a policyholder by considering its historical primary and excess losses. The optimal split point is derived based on the mean squared error criterion. We show when and why splitting a policyholder’s historical losses into primary and excess parts work analytically. In addition, we derived formulas for estimating our model parameters nonparametrically. Finally, we show the application of our model through three examples.

Summary for Lay Audience

Credibility theory is a set of quantitative tools that allows an insurer to adjust premiums based on policy holders’ past loss experience. The theory features the combination of data with other information, such as the mean loss of policyholders in the same rating class.
In this thesis, we introduce a two-dimensional semi-linear credibility model, which considers policyholders’ small losses and large losses separately. Our model is an extension of the classical credibility or split credibility models used by practicing actuaries.

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