Free random Lévy variables and financial probabilities

Zdzisław Burda, Jerzy Jurkiewicz, Maciej A. Nowak, G. Papp, Ismail Zahed

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We suggest that Free Random Variables, represented here by large random matrices with spectral Lévy disorder, may be relevant for several problems related to the modeling of financial systems. In particular, we consider a financial covariance matrix composed of asymmetric and free random Lévy matrices. We derive an algebraic equation for the resolvent and solve it to extract the spectral density. The free eigenvalue spectrum is in remarkable agreement with the one obtained from the covariance matrix of the SP500 financial market.

Original languageEnglish
Pages (from-to)181-187
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume299
Issue number1-2
DOIs
Publication statusPublished - Oct 1 2001

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random variables
Random Matrices
Covariance matrix
Random variable
Spectral Density
Financial Markets
Resolvent
Algebraic Equation
Disorder
Eigenvalue
eigenvalues
Modeling
disorders
matrices

Keywords

  • Financial analysis
  • Lévy processes
  • Random matrix models

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Free random Lévy variables and financial probabilities. / Burda, Zdzisław; Jurkiewicz, Jerzy; Nowak, Maciej A.; Papp, G.; Zahed, Ismail.

In: Physica A: Statistical Mechanics and its Applications, Vol. 299, No. 1-2, 01.10.2001, p. 181-187.

Research output: Contribution to journalArticle

Burda, Zdzisław ; Jurkiewicz, Jerzy ; Nowak, Maciej A. ; Papp, G. ; Zahed, Ismail. / Free random Lévy variables and financial probabilities. In: Physica A: Statistical Mechanics and its Applications. 2001 ; Vol. 299, No. 1-2. pp. 181-187.
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