Type of Document	Dissertation
Author	Zhang, Jianke
Author's Email Address	jizhang@math.fsu.edu
URN	etd-04042007-192630
Title	Numerical Methods for Portfolio Risk Estimation
Degree	Doctor of Philosophy
Department	Mathematics, Department of
Advisory Committee	Advisor Name Title Alec Kercheval Committee Member Fred Huffer Committee Member Kyle Gallivan Committee Member Paul Beamont Committee Member Warren Nichols Committee Member
Keywords	Weighted Orthogonal Procrustes Problem Portfolio Risk Total Risk Optimization Positive Definite
Date of Defense	2007-03-30
Availability	unrestricted
Abstract In portfolio risk management, a global covariance matrix forecast often needs to be adjusted by changing diagonal blocks corresponding to specific sub-markets. Unless certain constraints are obeyed, this can result in the loss of positive definiteness of the global matrix. Imposing the proper constraints while minimizing the disturbance of off-diagonal blocks leads to a non-convex optimization problem in numerical linear algebra called the Weighted Orthogonal Procrustes Problem. We analyze and compare two local minimizing algorithms and offer an algorithm for global minimization. Our methods are faster and more effective than current numerical methods for covariance matrix revision.
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