Free random Lévy variables and financial probabilities

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

Research output: Contribution to journalConference article

7 Citations (Scopus)


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
Issue number1-2
Publication statusPublished - Oct 1 2001
EventApplication of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic
Duration: Feb 8 2001Feb 10 2001


  • Financial analysis
  • Lévy processes
  • Random matrix models

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

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