Completing Partly-known Correlation Matrices to Optimize Insurance Capital

Dan Georgescsu (The Bank of England)


Calculations of regulatory required capital for insurers allow
for diversification between risks, which typically involves the
specification of dependency relations in the form of a correlation
matrix. However, it is often the case that not all of the entries in the
correlation matrix are known, which introduces uncertainty around the range
of potential capital outcomes. I show how to estimate upper and lower
bounds on capital requirements by formulating the problem as a semidefinite
programming problem. Another application is Integration Technique 2 of the
Solvency II regulations, which requires that the most onerous correlation
matrix is found, turning multiple correlation matrices of subsets of risks
into one large matrix which needs to be completed so that no other valid
completion results in a higher capital requirement.
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