## 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

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Smith, Llewellyn Hillyer, "Discrete Time Risk Models With Random Premiums" (2018). *Mathematics Dissertations*. 90.

https://mavmatrix.uta.edu/math_dissertations/90

## Comments

Degree granted by The University of Texas at Arlington