A review of mathematical models for pricing, risk, and optimization in cryptocurrency analytics

Abstract

The rapid expansion of cryptocurrencies and decentralized finance (DeFi) has redefined global financial systems, creating new challenges in asset pricing, risk measurement, and systemic stability. This study conducts a comprehensive review of 93 peer-reviewed articles published between 2019 and 2024 to consolidate the fragmented literature on mathematical models applied to cryptocurrencies and DeFi platforms. Using a mixed bibliometric–systematic approach based on the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) framework, the review integrates performance indicators, conceptual mapping, and qualitative synthesis to identify methodological advances and research trends. The findings reveal a progressive convergence between econometric models, such as the Generalized Autoregressive Conditional Heteroskedasticity (GARCH), stochastic volatility, and Lévy processes, and data-driven approaches based on machine learning (ML), deep learning (DL), and reinforcement learning (RL). These hybrid frameworks enhance predictive accuracy and adaptability in high-frequency and non-linear blockchain markets. The review also highlights optimization-based decision models that integrate Conditional Value-at-Risk (CVaR), network theory, and portfolio analytics for decentralized finance operations. However, interpretability, governance, and environmental sustainability remain underexplored dimensions. The study contributes by classifying mathematical approaches to pricing, volatility, and risk propagation, identifying methodological gaps, and recommending future research on explainable artificial intelligence (AI), environmental and cyber-risk modeling, and real-time validation for transparent and resilient decentralized financial ecosystems. • Review 93 studies analyzing mathematical models in cryptocurrency and digital finance systems. • Identify emerging methods for pricing, risk, and portfolio decisions under high volatility. • Compare deep learning models to traditional methods for forecasting and risk evaluation. • Evaluate decision models that include environmental, risk, and governance factors. • Recommend future research on interpretable tools for real-time decision-making.