Value-at-Risk (VaR) and Expected Shortfall (ES) are common high quantile-based risk measures adopted in financial regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk events (MPMR) that can occur over a length of time....

Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time. Many interesting models have been proposed to account for...

This study provides an explanation for the emergence of power laws in asset trading volume and returns. We consider a two-state model with binary actions, where traders infer other traders' private signals regarding the value of an asset from their actions and adjust their own behavior...

Power laws in productivity and firm size are well documented empirical regularities. As they are upper right-tail phenomena, this paper shows that assuming asymptotic power functions for various model primitives (such as demand and firm heterogeneity) are sufficient for matching these...

We develop an analytical framework designed to solve and analyze heterogeneous‐agent models that endogenously generate fat‐tailed wealth distributions. We exploit the asymptotic linearity of policy functions and the analytical characterization of the Pareto exponent to augment the...