Parameter uncertainty for integrated risk capital calculations based on normally distributed subrisks

In this contribution we consider the overall risk given as the sum of random subrisks $\mathbf{X}_j$ in the context of value-at-risk (VaR) based risk calculations. If we assume that the undertaking knows the parametric distribution family subrisk $\mathbf{X}_j=\mathbf{X}_j(θ_j)$, but does not know the true parameter vectors $θ_j$, the undertaking faces parameter uncertainty. To assess the appropriateness of methods to model parameter uncertainty for risk capital calculation we consider a criteri...