Actuarial Risk Matrices: The Nearest Valid Matrix Problem

Covariance and correlation matrices for insurance risk sources are often constructed from outputs of disparate models and manually manipulated by actuaries (often adjusted upwards to confer prudence as to potential losses from correlated sources). The disadvantage of such processes is that the resulting matrix is often no longer mathematically valid and cannot be inverted (technically we say it is not positive semi definite). This is problematic in using it in statistical models. This presentation looks at identifying the closest matrix to the original that is still mathematically valid for modelling. We show a range of results and methods for a variety of real data sets based on a research collaboration with Tokio Marine Kiln.

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