Bayesian Risk Aggregation: Correlation ... - ERM Symposium

Pairwise correlation priors As we describe in more detail in Section 5, a well-
established approach for the subjective determination of a prior density is by matching a
given functional form. The shape of the prior reflects the amount and the quality of the
available information and should match the experts’ beliefs as closely as possible.
As risk managers are concerned about unreasonable and possibly incorrect diversifi-
cation benefits, it is normally assumed that correlations between different risk types are
non-negative. Such a boundary condition for the correlation matrix can easily and natu-
rally be modelled within the Bayesian framework by considering only pairwise priors πi
that have support in [0,1].
Example 3.1. [Uniform prior]
Assume that the experts are totally uninformed about the possible values of the single
pair correlations ri for i = 1, . . . , 6. Consequently, we may want to take all values of ri as
equally likely and, in consideration of the general restriction ri ∈ [0, 1], a natural diffuse
prior is the uniform distribution
πi(ri) ∝ 1{0