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When does the Perron Frobenius result hold for correlation matrices?


Phelim Boyle, Lazaridis School of Business and Economics, Wilfrid Laurier University 

Phelim Boyle is an actuary whose research work in finance and insurance has won international recognition. He uses mathematical methods to solve problems at the interface of these fields. Boyle has made pioneering contributions to quantitative finance and his ideas have transformed how actuaries handle financial risk. His research has influenced financial practice by providing sophisticated tools for financial institutions to better manage their risks




This talk investigates conditions under which correlation matrices have a strictly positive dominant eigenvector. The sufficient conditions, from the Perron-Frobenius theorem, are that all the matrix entries are positive. The conditions for a correlation matrix with some negative entries to have a strictly positive dominant eigenvector are explored. The special structure of correlation matrices permits us to obtain analytical results for low dimensional matrices. Some specific results for the n-by-n case are also derived. This problem was motivated by an application in portfolio theory.



Friday, January 24, 2020


3 p.m.


LH 2064 (Lazaridis Hall)

Unknown Spif - $key