Structure methods for solving the nearest correlation matrix problem

Suliman Al-Homidan; Munirah AlQarni

doi:10.1007/s11117-012-0180-x

Structure methods for solving the nearest correlation matrix problem

Suliman Al-Homidan^*, Munirah AlQarni

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

The nearest correlation matrix problem is to find a positive semidefinite matrix with unit diagonal, that is, nearest in the Frobenius norm to a given symmetric matrix A. This problem arises in the finance industry, where the correlations are between stocks. In this paper, we formulate this problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Other methods are also studied. Comparative numerical results are reported.

Original language	English
Pages (from-to)	497-508
Number of pages	12
Journal	Positivity
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/s11117-012-0180-x
State	Published - Sep 2012

Keywords

Alternating projections method
Correlation matrix
Nearness problem
Newton method
Positive semidefinite programing
Semidefinite matrix

ASJC Scopus subject areas

Analysis
Theoretical Computer Science
General Mathematics

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10.1007/s11117-012-0180-x

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title = "Structure methods for solving the nearest correlation matrix problem",

abstract = "The nearest correlation matrix problem is to find a positive semidefinite matrix with unit diagonal, that is, nearest in the Frobenius norm to a given symmetric matrix A. This problem arises in the finance industry, where the correlations are between stocks. In this paper, we formulate this problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Other methods are also studied. Comparative numerical results are reported.",

keywords = "Alternating projections method, Correlation matrix, Nearness problem, Newton method, Positive semidefinite programing, Semidefinite matrix",

author = "Suliman Al-Homidan and Munirah AlQarni",

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doi = "10.1007/s11117-012-0180-x",

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AU - AlQarni, Munirah

PY - 2012/9

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AB - The nearest correlation matrix problem is to find a positive semidefinite matrix with unit diagonal, that is, nearest in the Frobenius norm to a given symmetric matrix A. This problem arises in the finance industry, where the correlations are between stocks. In this paper, we formulate this problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Other methods are also studied. Comparative numerical results are reported.

KW - Alternating projections method

KW - Correlation matrix

KW - Nearness problem

KW - Newton method

KW - Positive semidefinite programing

KW - Semidefinite matrix

UR - https://www.scopus.com/pages/publications/84867034777

U2 - 10.1007/s11117-012-0180-x

DO - 10.1007/s11117-012-0180-x

M3 - Article

AN - SCOPUS:84867034777

SN - 1385-1292

VL - 16

SP - 497

EP - 508

JO - Positivity

JF - Positivity

IS - 3

ER -

Structure methods for solving the nearest correlation matrix problem

Abstract

Keywords

ASJC Scopus subject areas

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