Portfolio Construction in Crypto Markets Using Generalized Maximum Entropy Models

Traditional portfolio optimization models, predominantly based on the mean–variance paradigm, often fall short in addressing the complexities of real-world financial markets, especially under distributional uncertainty and tail-risk exposure. In this paper, we propose a unified entropic framework for portfolio diversification grounded in three generalized entropy measures: Tsallis entropy, Rényi entropy, and Kaniadakis entropy. Each of these formulations extends Shannon’s classical entropy by introducing param-eters that govern sensitivity to concentration, asymmetry, and systemic uncertainty, thereby enabling more flexible control over portfolio structure. We formulate and solve the maximum entropy optimization problem under standard constraints of capital allocation and target return. The empirical validation is conducted on a selected portfolio of five major Nasdaq-listed assets—Apple (AAPL), Microsoft (MSFT), Nvidia (NVDA), Amazon (AMZN) and Tesla (TSLA)—using weekly return data from January to March 2025. Our results reveal that the generalized entropy models yield distinct diversification patterns, with Tsallis and Kaniadakis formulations offering more aggressive penalization of dominant weights and improved robustness under high vol-atility. In particular, the Kaniadakis entropy model, introduced here, provides a novel balance between structural resilience and statistical flexibility. This study enhances the current body of knowledge by demonstrating how generalized entropy measures can systematically improve diversification beyond the limitations of variance and even classical entropy. The proposed framework offers both theoretical rigor and practical relevance for asset managers operating in uncertain, nonlinear, and data-sparse envi-ronments.