BSc in Mathematics-Physics

Universite des Sciences et Techniques de Masuku

BSc Honours in Pure Mathematics

University of the Witwatersrand

MSc in Pure Mathematics

University of the Witwatersrand

M.Com in Financial Economics

University of Johannesburg

Ph.D. in Pure Mathematics
University of Johannesburg

MATH2415

Prof Ur Koumba is deeply dedicated to achieving excellence in both teaching and research. With a wealth of experience in higher education, his formal teaching journey commenced at the University of Johannesburg, where he earned his Ph.D. in Pure Mathematics in 2014 and a Master's in Financial Economics in 2018.

He firmly believes that students should approach their educational journey with a strong commitment to hard work and personal responsibility to attain their academic aspirations. He envisions an effective instructor as someone who can foster a learning environment that is both stimulating and supportive, all while infusing an element of enjoyment into the process. Recognizing that learning is an active endeavor requiring motivation, effort, and perseverance, Ur Koumba successfully taught various mathematics courses at different levels. His repertoire includes Real Analysis, Calculus I and II, Discrete Mathematics, Functional Analysis, Set Theory, and Mathematics for Economics.

Beyond the realm of teaching, Prof Koumba has exhibited leadership skills through his involvement in various social organizations. He also served as the Subject Head of the Mathematics department and as a Program Director at the University of the Free State in South Africa.

Ur's research agenda centers on advancing the structural theory of Riesz operators within diverse Banach spaces. Furthermore, he aims to contribute to resolving challenges in financial market theory. He firmly believes that Functional Analysis holds significant potential in addressing contemporary economic issues. While mathematical models are prevalent in fields such as Microeconomics, Macroeconomics, international trade, economic development, and public finance, they are grounded in general observations rather than direct empirical evidence. This limitation restricts their ability to provide explanations or predict phenomena not yet observed. Consequently, Prof. Ur Koumba highlights the need to address these limitations through Data Analytics, as the world grapples with economic challenges exacerbated by mathematical assumptions that may not align with reality in journals and theoretical conclusions.

Ur Koumba’s research focuses on advancing the structural theory of Riesz operators in various Banach spaces and addressing financial market theory challenges. He believes the merging of Data Analytics will have a significant impact in addressing financial issues such risk portfolio optimization.

Recent Publications

1. C. Mudzingiri & U. Koumba, Eliciting risk preferences experimentally versus using a general risk question. Does financial literacy bridge the gap? Risks 2021, 9, 140. https://doi.org/10.3390/risks9080140.
2. K.A. Ababio, J.C. Mba & U. Koumba, Optimisation of mixed assets portfolio using copula differential evolution: A behavioural approach, Cogent Economics and Finance, DOI 10.1080/23322039.2020.1780838, 2332-2039 (2020).
3. U. Koumba, C. Mudzingiri & J. C. Mba, Does uncertainty predict cryptocurrency return? A copula based approach, Macroeconomics and Finance in Emerging Market Economies, 1752-0851 (2019).
4. J. C. Mba, E. Pindza & U. Koumba, A differential evolution copula-based approach for a multi-period cryptocurrency portfolio optimization, Financial Markets and Portfolio Management, Springer, vol. 32(4), 399-418 (2018).
5. B.D. Simo-Kengne, K.A. Ababio, J.C. Mba & U. Koumba, Behavioural Portfolio selection and Optimisation: An application to International Stock, Financial Markets and Portfolio Management, Management Volume 32, Issue 3, 311-328 (2018).
6. D. Simo-Kengne, K.A. Ababio, J.C. Mba, U. Koumba, & M. Molepo, Risk, Uncertainty and Exchange Rate Behavior in South Africa, Journal of African Business (2017).
7. B.D. Simo-Kengne, K. A Ababio, J Mba & U Koumba, Multivariate Dependence Risk and Portfolio Selection: An Application to International Stock Portfolio. Available at SSRN: ttps://ssrn.com/abstract=2856364 (October 20, 2016).
8. U. Koumba & H. Raubenheimer, Positive Riesz Operators, Mathematical Proceedings of the Royal Irish Academy, Vol (115A), No 1 (2015) 39-49.
9. U. Koumba & H. Raubenheimer, Finite Rank Riesz Operators, Glasgow Math. J., Vol (56), 183–185 (2014).

Current working paper

1. U. Koumba, N.R. Loufouma Makala & R.O. Ocaya, Quasi inessential elements on ultrapowers of Banach algebras.
2. U. Koumba, On Finite Rank Riesz Operators.
3. U. Koumba, R. O. Ocaya, J. C. Mba, B.D. Simo-Kengne & K. Agyarko Ababio, Stress testing VaR modeling: Evidence from developed and emerging markets.