Date of Completion

8-7-2020

Embargo Period

8-7-2020

Keywords

Random effects, Predictive analytics, Dependence modeling, Credibility, General insurance

Major Advisor

Emiliano A. Valdez

Associate Advisor

Guojun Gan

Associate Advisor

Dipak K. Dey

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

In the ratemaking for general insurance, calculation of the pure premium has traditionally been based on modeling frequency and severity separately. It has also been a standard practice to assume, for simplicity, the independence of loss frequency and loss severity. However, in recent years, there is a sporadic interest in the actuarial literature and practice to explore models that depart from this independence assumption. Besides, because of the short-term nature of many lines of general insurance, the availability of data enables us to explore the benefits of using random effects for predicting insurance claims observed longitudinally, or over a period of time.

This thesis advances work related to the modeling of compound risks via random effects. First, we examine procedures for testing random effects using Bayesian sensitivity analysis via Bregman divergence. It enables insurance companies to judge whether to use random effects for their ratemaking model or not based on observed data. Second, we extend previous work on the credibility premium of compound sum by incorporating possible dependence as a unified formula. In this work, an informative dependence measure between the frequency and severity components is introduced which can capture both the direction and strength of possible dependence. Third, credibility premium with GB2 copulas are explored so that one can have a succint closed form of the credibility premium with GB2 marginals and explicit approximation of credibility premium with non-GB2 marginals. Finally, we extend microlevel collective risk model into multi-year case using the shared random effect. Such framework includes many previous dependence models as special cases and a specific example is provided with elliptical copulas. We develop the theoretical framework associated with each work, calibrate each model with empirical data and evaluate model performance with out-of-sample validation measures and procedures.

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