Graduation Semester and Year
Spring 2025
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Andrzej Korzeniowski
Abstract
Risk processes typically emerge in insurance and finance and are concerned with stochastic representation of uncertainties of real-world events. Main objective amounts to quantifying the chances of both desirable and undesirable events and balancing their mutual impact for the purpose of developing models that in some sense optimize the outcome from the business perspective. Our research is concerned with studying the evolution of the surplus process in which time and assets are integer-valued. Initial capital, random premiums, random claims, dividend payments based on assets’ performance constitute the components of our model. Our findings established recursive formulas for the total expected discounted dividend on finite and infinite time horizon. Furthermore, we introduced a novel investment strategy that is superior when compared to only dividend option in the sense that the combined investment-dividend option provides higher total returns for both the insurer and the shareholders. Finally, estimates of the probability of ruin, i.e., when the surplus process becomes negative, are also given.
Keywords
Discrete time surplus process, Random premiums, Dividend barrier, Total expected discounted dividends prior to ruin, Investment strategy
Disciplines
Other Applied Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Recommended Citation
Dangbe, Enoch J., "Discrete Time Risk Processes with Stochastic Premiums and Dividends" (2025). Mathematics Dissertations. 260.
https://mavmatrix.uta.edu/math_dissertations/260