Date of Award

2009

Degree Type

Report

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Daniel Coster

Abstract

Our thesis includes 2 sections. In section 1, we mainly discuss the distribution function and the empirical simulation of the total claims amount for a portfolio with multiple distributional assumptions, under the collective risk model for a single period.

In section 2, we discuss the collective risk model for an extended period, which mainly deals with the amount of surplus over several periods of time. Let Un denote the surplus at time n, then we interested in the probability of ruin, that is, the probability that there exists an n such that Un< O. In this section, we put forward an algorithm for the probability of ruin (both theoretical and empirical) using this model, with various distributional assumptions, and compare the theoretical and empirical results.

The reference of this project is Actuarial Mathematics, Newton L Bowers, Jr. et al, published by the Society of Actuaries, 1997.

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