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Nearest correlation matrix with constraints : a problem from finance

Charles, Benjamin
(2023)

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Details

Supervisors
Absil, Pierre-Antoine ; Antoine Vandendorpe
Faculty
Ecole polytechnique de Louvain
Degree label
Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée
Abstract
Given a partially specified matrix, we are interested in transforming it such that we can fill the unspecified values and obtain a positive semidefinite matrix. This problem arises in finance where the specified values in the matrix correspond to correlations between stocks. This master thesis is in collaboration with BNP Paribas. We are particularly interested in transforming the partially specified matrix such that the fewest specified elements are modified. To do that, we developed two new algorithms that both rely on semidefinite optimization. The first algorithm is more robust and can be used with a larger range of partially specified matrices. The second algorithm is designed to be efficient for partially specified matrices that can be represented by chordal graphs. Both algorithms are designed to be efficient for partially specified matrices of size similar as the one provided by BNP Paribas (200x200) and are not applicable for large-scale problems.