Multifractal Model of Asset Returns: a view from linear algebra and convex analysis
Abstract
The Multifractal Model of Asset Returns (MMAR) proposes a class of the so-called multifractal processes for modelling of financial returns.
Introduced by Mandelbrot, Fisher and Calvet in late 90ties this model reduced the problem of asset returns to computing the local regularity of certain self-similar functions and curves (or, more generally, distributions). Actually, this extends the well-known notion of affine fractals introduced by J.Hutchinson in 1980 to study some financial models.
Using tools of linear algebra and convex analysis we show how to apply elementary linear algebra to this problem. In particular, the extremal values of the local regularity are related to the so-called joint spectral radius of finite-dimensional matrices, whose efficient estimation is one of the most intriguing problem of computational mathematics now. The computing of average values of the local regularity leads to the Lyapunov exponent of linear operators.
The main results are formulated in quite elementary terms of linear algebra and convex geometry, no deep special knowledge is required from the listeners.
Information: Igor Pouchkarev pouchkarev@few.eur.nl
