Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E

Mandelbrot is world-renowned for his work in fractal geometry. This bo ok introduces the path-breaking notion that financial prices follow a fractional Brownian motion in multifractal time. That model combines f ractional Brownian motion and multifractals, both of which Mandelbrot pioneered around 1970, with the notion of self-affine scale invariance , which he applied to financial prices around 1960. The new model acco unts for long dependence and long tailedness, the latter being a token of concentration and even discontinuity. Both features characterize f inancial prices and are essential to the understanding and measurement of risk.