Robust Entropy Portfolio Optimization in Crypto Markets

Traditional portfolio optimization models primarily address two key dimensions: risk and return. This paper extends the classical Markowitz framework by integrating a third critical factor—liquidity—captured via second-order Tsallis entropy. We intro-duce a novel mean–variance–entropy model that flexibly assigns weights to return and entropy, enabling diversified asset allocations tailored to investor preferences. Entropy is interpreted not only as a statistical measure of diversification but also as a structural proxy for portfolio liquidity, acting as a soft constraint that mitigates overconcentra-tion in volatile assets. Analytical portfolio solutions are derived using a Lagrangian formulation, offering interpretable allocations in both two- and three-asset scenarios. The model is empirically validated on a cryptocurrency dataset comprising Bitcoin (BTC), Ethereum (ETH), and Solana (SOL) over the January–March 2025 period. Re-sults indicate that entropy-driven diversification enhances portfolio balance and ro-bustness, even with limited historical data. In contrast to traditional models, the pro-posed approach facilitates explicit trade-offs between expected return and stability, offering practical advantages in fast-moving and uncertainty-prone financial envi-ronments. This study contributes to the literature by presenting a robust, entro-py-based optimization framework for liquidity- sensitive portfolio construction, with direct applicability to crypto asset management.