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. 216.
https://mavmatrix.uta.edu/math_dissertations/216
Comments
Degree granted by The University of Texas at Arlington