Truth routinely manifests itself through mathematics. Just as law uses words to animate its enterprise, nature speaks through the language of mathematics. Through this volume, Illustrating Finance Policy with Mathematica, Nicholas L. Georgakopoulos enriches the Palgrave Macmillan, series,...

This essay presents higher-moment asset pricing, a generalized approach to finance that combines a mathematically informed understanding of economic fundamentals with psychologically and biologically inspired behavioral insights. It ultimately seeks to apply higher-moment asset pricing to a wide...

This article reviews two leading measures of financial risk and an emerging alternative. Embraced by the Basel accords, value-at-risk and expected shortfall are the leading measures of financial risk. Expectiles offset the weaknesses of value-at-risk (VaR) and expected shortfall. Indeed,...

The law of regulated industries, particularly the legislative command that the government ensure “just and reasonable rates” for regulated services, is a highly specialized application of financial economics. Ratemaking, to put it bluntly, represents a regulatory exercise in capital asset...

In her 2017 book, Rules for a Flat World, Gillian Hadfield upbraids the legal profession and the legal academy for ascribing supremacy, even exclusivity, to traditional legal institutions. Legal infrastructure, especially in the poorest countries, depends on entrepreneurs willing to shatter...

My recent book, Econophysics and Capital Asset Pricing: Splitting the Atom of Systematic Risk, splits beta, the capital asset pricing model's basic unit of systematic risk, into subatomic (or “baryonic”) components, by analogy to the Standard Model of particle physics. This essay offers...

This essay seeks to rehabilitate the capital asset pricing model by splitting beta, the basic unit of systematic risk, into subatomic (or “baryonic”) components. By analogy to quantum chromodynamics and other aspects of the Standard Model of particle physics, this essay bifurcates beta on...

A stretched exponential function taking the form, f(x) = exp(-x^β), x ∈ [0, ∞), β ∈ (0, 1], characterizes decay, diffusion, and relaxation phenomena known as Kohlrausch-Williams-Watts (KWW) processes. Recent work, particularly on relaxation kinetics in metallic glasses, has described the...

Unsupervised machine learning can interpret logarithmic returns and conditional volatility in commodity markets. k-means and hierarchical clustering can generate a financial ontology of markets for fuels, precious and base metals, and agricultural commodities. Manifold learning methods such as...

Machine-learning regression models lack the interpretability of their conventional linear counterparts. Tree- and forest-based models offer feature importances, a vector of probabilities indicating the impact of each predictive variable on a model’s results. This brief note describes how to...