Application of Uncertain Rényi Entropy as a Metric for Risk in Portfolio Optimization

This research presents an innovative multi-objective framework for portfolio optimization that employs uncertain space, diverging from conventional probability space and information theory, and moving away from traditional risk assessment metrics such as variance. The models examined and discussed predominantly operate within the probability space, necessitating access to historical data, which is a problem for public investors. The proposed approach seeks to simultaneously maximize the expected value of uncertain returns and minimize Rényi entropy, which indicates portfolio risk. The Rényi entropy represents a generalized form of established entropy measures, characterized by a variable parameter “v”. This flexibility allows it to more effectively capture the tail behavior of return distributions, often overlooked when relying solely on variance. This shift in perspective can enhance the ability to identify and mitigate risks in various financial contexts. Tree meta-heuristic optimization techniques are employed to tackle this uncertain Rényi entropy-mean portfolio optimization (REMPO) challenge. In conclusion, a comparative analysis with the Markowitz Model and another model utilizing Shannon entropy reveals that the portfolio derived from the suggested model consistently outperforms in terms of returns while exhibiting reduced risk across all specified parameters.