ORCID Identifier(s)

0000-0003-1845-1144

Graduation Semester and Year

2018

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Andrzej Korzeniowski

Abstract

Over the past century insurance companies relied to a large extent on the continuous time Mathematical Risk Model proposed by Lundberg, known for its ability to estimate the probability of ruin(capital reserve falling below zero), given the initial capital, linear premium rate and cumulative random size claims occurring at random times. In this Dissertation we introduce a discrete time risk model that allows random premiums, and derive the estimates of the ruin probabilities on both finite and infinite time horizons. Tools applied are drawn from modern probability and include,Martingales, Invariance Principle for Brownian motions, and Large Deviation Principle for the asymptotics of rare events. Our considerations can be dubbed “end of the day model”, as ruin is neither declared nor acted upon when it falls between successive discrete times.

Keywords

Mathematical risk theory, Insurance mathematics

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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