Meet Ugochukwu Oliver Adiele, a UNT mathematics graduate student completing his dissertation research under the guidance of Dr. Kai-Sheng Song, conducting research on models for pricing financial derivatives in cases where the underlying asset return dynamics follow a Levy process. Ugochukwu explains, "A Levy process is essentially a time-dependent random variable with discontinuities, possessing several favorable properties that make them suitable for modeling several phenomena associated with the financial markets amongst other things."

As one of the recipients of the Dean's Doctoral Summer Research Stipend this year, Ugochukwu has been able to prioritize his doctoral work through the summer months.

"This award has paved the way for me to pursue my academic dreams, instilling in me a greater sense of confidence and motivation to strive for excellence," he said. "Moreover, it has brought me one step closer to achieving my aspirations and making a positive impact on my community. For these reasons, I am profoundly grateful to the donors."

Ugochukwu received his undergraduate degree from the University of Lagos in Nigeria. He said that deciding to attend UNT after that was an easy choice.

"The mathematics faculty at UNT consists of some of the most brilliant mathematicians in the field," he said. "Over the years, I closely followed the research activities of a couple of them, so coming to UNT was a natural outcome of my keen interest in their research endeavors."

In 2021, Ugochukwu enrolled in a course at UNT at the 6000 level, instructed by Dr. Kai-Sheng Song. The content of this course revolved around the subject matter of mathematical finance and time series analysis.

"As a part of the ongoing assessment within this course, I was required to compose and deliver a report based on a classical article authored by Robert Merton, titled 'Option pricing when underlying stock returns are discontinuous,'" he said. "Through this article, I gained exposure to practical applications of diverse abstract mathematical concepts. Specifically, it acquainted me with intriguing applications of advanced mathematical principles such as measure theory, stochastic calculus, and mathematical structures such as martingales and Levy Processes."

These applications are instrumental in addressing complex issues encountered in finance and econometrics, and advancements in these fields hold the potential to improve risk management practices for participants in financial markets, including both buyers and sellers.

"This is partly because hedging is a fundamental element of risk management in financial markets," said Ugochukwu. "In my opinion, the effectiveness of a hedging strategy is directly influenced by how well the model approximates the true nature of the underlying risky assets."

Ugochukwu said one of the most rewarding aspects of doing this research is witnessing the progression of an idea from curiosity to forming actionable research questions he can seek answers to. This process is made possible with the help of his mentors, UNT mathematics professors Dr. Song and Dr. Iaia.

"Dr. Song's mentorship has greatly enhanced my understanding of the intricacies of formulating specific research questions to uncover valuable insights within a research project," he said. "And Dr. Iaia's influential teaching methods have profoundly influenced how I structure my own courses."

After receiving his PhD, Ugochukwu envisions himself in a quantitative research role at a financial institution or an academic position at a research university. He said that being part of such an intelligent, caring, and supportive community at UNT has made it easy accomplish his goals.

"UNT's mathematics department is one such community, and being here has contributed immensely to reducing the stress typically associated with pursuing an advanced degree of this nature," he said.

The Dean's Doctoral Summer Research Stipend provides COS graduate students with time to concentrate on their research over the summer and accelerate their dissertation completion. Help us further support world-changing graduate research at the UNT College of Science by making a donation to this fund today: https://cos.unt.edu/help-support-graduate-research-unt