Free random Lévy variables and financial probabilities

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

doi:10.1016/S0378-4371(01)00294-1

Free random Lévy variables and financial probabilities

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

Physics and Astronomy

Jagiellonian University in Kraków
Bielefeld University
Eötvös Loránd University

Research output: Contribution to journal › Conference article › peer-review

7 Scopus citations

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 language	English
Pages (from-to)	181-187
Number of pages	7
Journal	Physica A: Statistical Mechanics and its Applications
Volume	299
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4371(01)00294-1
State	Published - Oct 1 2001
Event	Application of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic Duration: Feb 8 2001 → Feb 10 2001

Keywords

Financial analysis
Lévy processes
Random matrix models

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10.1016/S0378-4371(01)00294-1

Cite this

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title = "Free random L{\'e}vy variables and financial probabilities",

abstract = "We suggest that Free Random Variables, represented here by large random matrices with spectral L{\'e}vy 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 L{\'e}vy 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.",

keywords = "Financial analysis, L{\'e}vy processes, Random matrix models",

author = "Zdzis{\l}aw Burda and Jerzy Jurkiewicz and Nowak, \{Maciej A.\} and G{\'a}bor Papp and Ismail Zahed",

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journal = "Physica A: Statistical Mechanics and its Applications",

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TY - JOUR

T1 - Free random Lévy variables and financial probabilities

AU - Burda, Zdzisław

AU - Jurkiewicz, Jerzy

AU - Nowak, Maciej A.

AU - Papp, Gábor

AU - Zahed, Ismail

PY - 2001/10/1

Y1 - 2001/10/1

N2 - 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.

AB - 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.

KW - Financial analysis

KW - Lévy processes

KW - Random matrix models

UR - https://www.scopus.com/pages/publications/0035471697

U2 - 10.1016/S0378-4371(01)00294-1

DO - 10.1016/S0378-4371(01)00294-1

M3 - Conference article

AN - SCOPUS:0035471697

SN - 0378-4371

VL - 299

SP - 181

EP - 187

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-2

T2 - Application of Physics in Economic Modelling (NATO ARW)

Y2 - 8 February 2001 through 10 February 2001

ER -

Free random Lévy variables and financial probabilities

Abstract

Keywords

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