Si ChenFollow

Document Type

Thesis

Degree Name

Master of Science (MSc)

Department

Mathematics

Faculty/School

Faculty of Science

First Advisor

Dr. Zilin Wang

Advisor Role

Supervisor

Second Advisor

Dr. Mary Kelly

Advisor Role

Co-Supervisor

Abstract

The aggregate loss model has applications in various areas such as financial risk management and actuarial science. The aggregate loss is the summation of all random losses occurred in a period, and it is governed by both the loss severity and the loss frequency. While the impact of the loss severity on aggregate loss is well studied, less focus is paid on the influence of loss frequency on aggregate loss, which motivates our study. In this thesis, we enrich the aggregate loss framework by introducing the Poisson-Tweedie distribution as a candidate for modelling loss frequency, prove the closedness of Poisson-Tweedie under binomial-thinning, investigate bias of parameter and quantile estimation through simulation and apply our proposed model on real data to demonstrate its advantage. The Poisson-Tweedie distribution family contains many of the commonly used distributions for modelling loss frequency, thus making loss frequency fitting more flexible and reduce the chance of model misspecification. Apart from this feature, the Poisson-Tweedie family is also convolution closed, which allows us to use the same distribution family to model frequency data over different time lengths. The proven closedness under binomial thinning implies that the frequency distribution remains in the same family of Poisson-Tweedie when the observations have a reporting threshold, simplifying the parameter estimation for loss frequency. Through simulation studies, we investigate and find the impact of misspecification of the loss frequency distribution to the aggregate loss quantile, as well as a non-negligible bias of the maximum likelihood estimator of the family index of Poisson-Tweedie. Finally, we have applied our proposed model to Transportation Security Administration (TSA) Claims data to demonstrate modelling capacity on real-world problems.

Convocation Year

2020

Convocation Season

Spring

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