Non-homogeneous Risk Measures and Optimal Bank Leverage.

Abstract 

Although the Kelly criterion has had considerable success in financial applications, it often yields too risky strategies. Vince and Zhu (year) have proposed two alternative criteria (the inflection point, which determines the optimal marginal return, and the optimal return to risk) that still preserve Kelly-type properties and mitigate risk. However, these approaches do not deal with non-homogeneous risk measures, resulting in optimal bank leverage problems due to liquidation costs associated with deleveraging. In our research, we generalize the three criteria (Kelly point, inflection point, and return to risk) to the case of non-homogenous risk measures. We show the conditions for the existence of optimal leverage levels under the three criteria. This generalization is applied to the optimal bank leverage problem, considering liquidation costs, using real-world data. Finally, we conduct several tests to measure the impact of different inputs on the problem, such as the investment horizon, the expected return, and the maturity of the assets.  

Biographical Statement  

Sagara Dewasurendra, Ph.D. is an Assistant Professor of Mathematics at Indiana University-East. He received his Ph.D. degree in mathematics (minor in statistics) from Western Michigan University in June 2019. Financial mathematics, optimization, and mathematical modeling are my areas of research interest. For the last few years, he has been working on optimization with Growth Optimal Portfolio, also known as Kelly Criterion, and its application in bank leverage level with Dr. Pedro Judice, a senior researcher, a bank manager in Portugal and Professor Qiji Zhu (WMU). We have published our early works in the Risks Journal MDPI. This work is an extension of my Ph.D. thesis. He has presented his previous works related to the Optimal Bank Leverage Level at the Midwest Optimization Meeting conference in the last three years. He is also pursuing to become a professionally qualified Associate of the Society of Actuaries (ASA).