Date of Completion

1-26-2015

Embargo Period

1-20-2015

Keywords

Longitudinal data, Random-effects models, Multivariate outcomes, Run-off triangle, Copula, Insurance Demand

Major Advisor

Professor Emiliano A. Valdez

Associate Advisor

Professor James G. Bridgeman

Associate Advisor

Professor Brian M. Hartman

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

Analysis of longitudinal data has increased in popularity in recent years for several disciplines that is commonly used to understand the dynamic nature and the heterogeneity within and among subjects. There has been a much more rapid progress of longitudinal analysis for univariate data. However, there is a developing interest of extending the longitudinal framework to handle multivariate responses for obvious reasons: to capture dependence structure of the responses and thereby to increase the efficiency of the model. Actuarial applications in this area are very limited at the moment and it is our hope to contribute to this developing literature. Most work has focused on the assumption of multivariate normal for the joint responses; we propose a more flexible framework of using copula functions to integrate the dependence among responses and the classical random effects approach to identify intertemporal dependence within a subject and unobservable subject-specific heterogeneity among observations. Covariate information is taken into account for observable subject-specific effects through the regression model for the marginals.

For empirical illustration, we analyzed two datasets which are directly related with the insurance industry. Our first data set is used to understand the global insurance demand in both life and non-life insurance. Simultaneously, we used the proposed models to understand the association between these two insurance lines. Loss triangles corresponding to four insurance lines have been considered under the second data set. We transformed loss triangle data into the longitudinal framework to apply the above mentioned new method. In both empirical studies, Archimedean and Elliptical family copulas are incorporated. To illustrate the flexibility of the proposed model, we have considered different skewed distributions, such as lognormal, GB2, and Weibull.

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