Dynamic copulas provide a flexible framework for modelling time-varying dependencies between financial assets, overcoming the limitations of traditional correlation measures and DCC models. Their ability to capture non-linear relationships, tail dependence, and asymmetry makes them particularly useful for risk management and portfolio optimization. The main contributions of this paper are: first, by extending dynamic specifications to the Student’s t, Clayton, and Frank copulas, and second, by providing their implementation in the R environment through the “dynCopula” package, freely available for the research community. Our empirical application considers three major international stock markets (Euro Stoxx 50, S&P 500, Nikkei) and Bitcoin. The results reveal that the dependence between assets evolves over time and intensifies during periods of financial stress. We also show that diversification benefits increase as the degree of dependence decreases, provided that assets have similar risk levels. Finally, dynamic copulas yield more accurate estimates of market risk than static models. These results underscore the benefits of dynamic copulas for practitioners: they enable more reliable risk quantification, enhance hedging strategies, and support the construction of optimal or minimum-variance portfolios under changing market conditions, making them a valuable tool for both investment management and financial risk analysis.

Short-selling is common in financial markets but is also strictly regulated. When short selling is banned, heterogeneous beliefs determine which investors take long positions and which have constrained positions of zero in equilibrium. Solving such models is computationally intensive. We set out three algorithms suited to solving models with very large numbers of investor types – such as millions – quickly on a standard laptop or desktop computer. The fastest algorithm combines price iterations with a divide and conquer approach. As an application we study the impact of a short-selling ban on price dynamics and wealth distribution in a market of many investor types in evolutionary competition, and we observe that both can be affected substantially.