Author: Gee Yul Lee

Publisher:

Published: 2017

Total Pages: 0

ISBN-13:

This dissertation contributes to the risk and insurance literature by expanding our understanding of insurance claims modeling, deductible ratemaking, and the insurance risk retention problem. In the claims modeling part, a data-driven approach is taken to analyze insurance losses using statistical methods. It is often common for an analyst to be interested in several outcome measures depending on a large set of explanatory variables, with the goal of understanding both the average behavior, and the overall distribution of the outcomes. The use of multivariate analysis has an advantage in a broad context, and the literature on multivariate regression modeling is extended with a focus on dependence among multiple insurance lines. In this process, a deductible is an important feature of an insurance policy to consider, because it may influence the frequency and severity of claims to be censored or truncated. Standard textbooks have approached deductible ratemaking using models for coverage modification, utilizing parametric loss distributions. In practice, regression could be used with explanatory variables including the deductible amount. The various approaches to deductible ratemaking are compared in this dissertation. Ultimately, an insurance manager would be interested in understanding the influence of a retention parameter change to the risk of a portfolio of losses. The retention parameter may be deductible, upper limit, or coinsurance. This dissertation contributes to the statistics and actuarial literature by introducing and applying the 01-inflated negative binomial frequency model (a frequency model for observations with an inflated number of zeros and ones), and illustrating how discrete and continuous copula methods can be empirically applied to insurance claims analysis. In the process, the dissertation provides a comparison among various deductible analysis procedures, and shows that the regression approach has an advantage in problems of moderate size. Finally, the dissertation attempts to broaden our understanding of the risk retention problem within a constrained optimization framework, and demonstrates the quasiconvexity of the objective function in this problem. The dissertation reveals that the loading factor of a reinsurance premium has a risk measure interpretation, and relates to the risk measure relative margins (RMRM). Concepts are illustrated using the Wisconsin Local Government Property Insurance Fund (LGPIF) data.