Explicit Solutions to Correlation Matrix Completion Problems, with an Application to Risk Management and Insurance

18 Pages Posted: 16 Oct 2017

See all articles by Dan Georgescu

Dan Georgescu

Bank of England - Prudential Regulation Authority

Nicholas Higham

University of Manchester

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Date Written: October 13, 2017

Abstract

We derive explicit solutions to the problem of completing a partially specified correlation matrix. Our results apply to several block structures for the unspecified entries that arise in insurance and risk management, where an insurance company with many lines of business is required to satisfy certain capital requirements but may have incomplete knowledge of the underlying correlation matrix. Among the many possible completions we focus on the one with maximal determinant. This has attractive properties and we argue that it is suitable for use in the insurance application. Our explicit formulas enable easy solution of practical problems and are useful for testing algorithms for the general correlation matrix completion problem.

Keywords: Matrix Completion, Correlation Matrix, Positive Definite Matrix, Maximal Determinant, Chordal Graph, Covariance Selection, Insurance, Risk Management

Suggested Citation

Georgescu, Dan and Higham, Nicholas and Peters, Gareth, Explicit Solutions to Correlation Matrix Completion Problems, with an Application to Risk Management and Insurance (October 13, 2017). Available at SSRN: https://ssrn.com/abstract=3054171 or http://dx.doi.org/10.2139/ssrn.3054171

Dan Georgescu (Contact Author)

Bank of England - Prudential Regulation Authority ( email )

20 Moorgate
London, EC2R 6DA
United Kingdom

Nicholas Higham

University of Manchester ( email )

Oxford Road
Manchester, M13 9PL
United Kingdom

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

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