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. / A Dissertation submitted to the Department of Mathematics in partial fulfillment of
the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2007. / Date of Defense: March 30, 2007. / Weighted Orthogonal Procrustes Problem, Portfolio Risk, Total Risk, Optimization, Positive Definite / Includes bibliographical references. / Alec Kercheval, Professor Directing Dissertation; Fred Huffer, Outside Committee Member; Kyle Gallivan, Committee Member; Paul Beaumont, Committee Member; Warren Nichols, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_168692 |
| Contributors | Zhang, Jianke (authoraut), Kercheval, Alec (professor directing dissertation), Huffer, Fred (outside committee member), Gallivan, Kyle (committee member), Beaumont, Paul (committee member), Nichols, Warren (committee member), Department of Mathematics (degree granting department), Florida State University (degree granting institution) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource, computer, application/pdf |
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