Completing Correlation Matrices at the Bank of England
Missing data, or lack of information, is a common problem in situations where we want to analyze processes, make predictions, assess risks, etc. One example is in the insurance industry, where a correlation matrix is used in the aggregation of risk exposures required by regulations, but some of the correlations are unknown.
On the Bank of England's blog, Bank Underground, Professor Nick Higham and Dan Georgescu (Head of Group Risk Internal Model Validation, Generali, Trieste, Italy), explain how to fill in the missing entries of a correlation matrix in a way (the maximum determinant completion) that has useful theoretical properties. This process is analogous to completing a Sudoku puzzle---but the size of the array can be much larger, perhaps in the thousands. They identify explicit solutions for some practically important cases, and also show how to treat the general problem using general-purpose optimization algorithms.
This work will appear in a paper co-authored with Professor Gareth Peters (Heriot Watt University) in the journal Royal Society Open Science.