A multi-objective uncertain portfolio optimization model based on tsallis entropy

Abstract

This work introduces a novel multi-objective framework for portfolio optimization that integrates un certainty theory with Tsallis 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 mean-Tsallis entropy portfolio optimization (UMTPO) model. This framework simultaneously maximizes uncertain returns and minimizes risk, which is quantified by Tsallis entropy. By using Tsallis entropy, a generalized form of Shannon entropy with a flexible parameter β, our model more effectively captures the tail behavior of return distributions, a limitation of conventional metrics like variance. To solve the proposed model, two classical approaches and two meta-heuristic algorithms are employed. Finally, a comparative analysis with the Markowitz model and a model based on Renyi entropy shows that the portfolio derived from the suggested model consistently outperforms in terms of returns while exhibiting reduced risk across all specified parameters.