Ascolta

Dr. Andres Garcia Medina

Centro de Investigación en Matemáticas, CIMAT-CONACYT Mexico

 

An introduction to random matrices and free probability in portfolio

theory: a data science approach.

 

Abstract:

A brief introduction will be given to the theory of random matrices from its origins in statistical physics to its most modern formulation using elements of free probability. From this perspective, the family of rotationally invariant estimators will be described, and applications within Markowitz portfolio theory will be discussed. At all times, data science tools and Python simulations will be used to develop insight into the theory.

 

 

Day 1 Monday 11/07/2011 15:00 Aula AP1, viale delle scienze, ed. 18:

Preliminary concepts of random matrices such as the semicircle law and the Marchenko-Pastur law will be reviewed. Its application in portfolio theory will be discussed. Finally, the code of its implementation will be described.

 

 

Day 2 Tuesday 12/07/2011 15:00 Aula AP1, viale delle scienze, ed. 18:

Concepts of classical probability will be reviewed to introduce elements of free probability as an analogy. Some transformations will be defined to determine the spectrum of products and sums of random matrices. Its application in portfolio theory will be discussed.

Finally, an application of the theory will be shown.