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

This research introduces a novel multi-objective framework for portfolio optimization that integrates uncertainty theory with Rényi entropy as a risk metric. Unlike traditional models that operate within a probability space and rely on historical data— a challenge for public investors— our approach leverages an uncertain space. Our primary contribution is the development of the Uncertain Rényi Entropy-Mean Portfolio Optimization (REMPO) model. This framework simultaneously maximizes uncertain returns and minimizes risk, which is quantified by Rényi entropy. By using Rényi entropy, a generalized form of other entropy measures with a flexible parameter “v”, our model more effectively captures the tail behavior of return distributions, a limitation of conventional metrics like variance. Three 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.