Abstract This paper presents a groundbreaking integration of Markov Decision Processes (MDPs) with fractional Ornstein-Uhlenbeck models incorporating jump dynamics for cryptocurrency portfolio optimization. We develop a comprehensive theoretical framework that captures the unique characteristics of cryptocurrency markets, including long-range dependence, heavy tails, and jump discontinuities. Using historical data from five major cryptocurrencies (Bitcoin, Ethereum, Ripple, Binance Coin, and Cardano) spanning from January 2020 to August 2025, we calibrate jump-diffusion models and implement a sophisticated MDP-based portfolio optimization strategy. Our empirical analysis reveals that cryptocurrency returns exhibit significant deviations from normality, with Student- t and Laplace distributions providing superior fits. The Hurst exponent analysis confirms persistent behavior across all assets, with values ranging from 0.555 to 0.573. Jump detection algorithms identify frequent discontinuous price movements, with jump frequencies between 8.95 % and 11.17 % of trading days. The proposed MDP-Jump strategy achieves superior performance with a total return of 236.95 % and Sharpe ratio of 1.117, significantly outperforming traditional strategies. These findings provide crucial insights for institutional investors and portfolio managers seeking to optimize cryptocurrency allocations while managing tail risks and jump dynamics.
Pindza et al. (Fri,) studied this question.