Robust Portfolio Optimization in Crypto Markets Using Second-Order Tsallis Entropy and Liquidity-Aware Diversification

Florentin Șerban () and Silvia Dedu
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Florentin Șerban: Department of Applied Mathematics, Bucharest University of Economic Studies, 010374 Bucharest, Romania
Silvia Dedu: Department of Applied Mathematics, Bucharest University of Economic Studies, 010374 Bucharest, Romania

Risks, 2025, vol. 13, issue 9, 1-18

Abstract: In this paper, we propose a novel optimization model for portfolio selection that integrates the classical mean–variance criterion with a second-order Tsallis entropy term. This approach enables a trade-off between expected return, risk, and diversification, extending Markowitz’s theory to account for non-Gaussian characteristics and heavy-tailed distributions that are typical in financial markets—especially in cryptocurrency assets. Unlike the first-order Tsallis entropy, the second-order version amplifies the effects of distributional structure and allows for more refined penalization of portfolio concentration. We derive the analytical solution for the optimal weights under this extended framework and demonstrate its performance through a case study using real data from selected cryptocurrencies. Efficient frontiers, portfolio weights, and entropy indicators are compared across models. This novel combination may improve portfolio selection under uncertainty, especially in the context of volatile assets such as cryptocurrencies, as the proposed model can provide a more robust and diversified portfolio structure compared to conventional theories.

Keywords: portfolio optimization; second-order Tsallis entropy; liquidity-aware models; risk and return trade-off; cryptocurrency investment; robust diversification (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jrisks:v:13:y:2025:i:9:p:180-:d:1751311

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