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,...

Econophysics applies the techniques of physics and nonlinear dynamics to complex economic problems. This essay invokes econophysics in order to introduce a theoretical model that aspires to encompass all essential features of real financial markets. It summarizes the central argument of my book,...

Quantitative finance traces its roots to modern portfolio theory. Despite the deficiencies of modern portfolio theory, mean-variance optimization nevertheless continues to form the basis for contemporary finance. The term "postmodern portfolio theory" expresses many of the theoretical advances...

This survey of portfolio theory, from its modern origins through more sophisticated, “postmodern” incarnations, evaluates portfolio risk according to the first four moments of any statistical distribution: mean, variance, skewness, and excess kurtosis. In pursuit of financial models that...