Entropy-Based portfolio optimization under Varma–Tsallis Statistics: Evidence from stock markets

In this paper, we propose a novel entropic portfolio model inspired by Cover’s universal portfolio framework, incorporating Tsallis statistics to generalize the traditional approach. Utilizing an (a,b)-deformed logarithmic function derived from Tsallis entropy, we introduce the concept of (a,b)-growth rate for stock market portfolios and extend it to the Varma–Tsallis entropic framework. Within this setting, we define the optimal (a,b)-growth rate and derive the growth-optimal portfolio that maximizes terminal (a,b)-wealth over n-trading periods. We further establish the asymptotic optimality of our approach, proving that the generalized logarithmic utility portfolio achieves expected returns at least as high as any other strategy under this entropy-based paradigm, ensuring long-run performance dominance. By introducing parameters that govern tail sensitivity and non-extensive entropy effects, our model provides a flexible alternative to conventional strategies. Empirical analyses demonstrate that the Varma–Tsallis portfolio not only adapts more effectively to complex market dynamics but also delivers competitive and often superior performance relative to benchmark Cover’s portfolio strategies, particularly during periods of financial turbulence.