Other Statistics and Probability Commons^™

On The Sparre-Andersen Risk Models, Ruixi Zhang

Electronic Thesis and Dissertation Repository

This thesis develops several strategies for calculating ruin-related quantities for a variety of extended risk models. We focus on the Sparre-Andersen risk model, also known as the renewal risk model. The idea of arbitrary distribution for the waiting time between claim payments arose in the 1950’s from the collective risk theory, and received many extensions and modifications in recent years. Our goal is to tackle model assumptions that are either too relaxed for traditional methods to apply, or so complicated that elaborate algebraic tools are needed to obtain explicit solutions.

In Chapter 2, we consider a Lévy risk process and …

Some Recent Developments On Pareto-Optimal Reinsurance, Wenjun Jiang

Electronic Thesis and Dissertation Repository

This thesis focuses on developing Pareto-optimal reinsurance policy which considers the interests of both the insurer and the reinsurer. The optimal insurance/reinsurance design has been extensively studied in actuarial science literature, while in early years most studies were concentrated on optimizing the insurer’s interests. However, as early as 1960s, Borch argued that “an agreement which is quite attractive to one party may not be acceptable to its counterparty” and he pioneered the study on “fair” risk sharing between the insurer and the reinsurer. Quite recently, the question of how to strike a balance in risk sharing between an insurer and …

Advances In Semi-Nonparametric Density Estimation And Shrinkage Regression, Hossein Zareamoghaddam

Electronic Thesis and Dissertation Repository

This thesis advocates the use of shrinkage and penalty techniques for estimating the parameters of a regression model that comprises both parametric and nonparametric components and develops semi-nonparametric density estimation methodologies that are applicable in a regression context.

First, a moment-based approach whereby a univariate or bivariate density function is approximated by means of a suitable initial density function that is adjusted by a linear combination of orthogonal polynomials is introduced. Such adjustments are shown to be mathematically equivalent to making use of standard polynomials in one or two variables. Once extended to apply to density estimation, in which case …