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

## Author

Listed:
• Andreas Frohlich
• Annegret Weng

## Abstract

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 $\mathbf{X}_j=\mathbf{X}_j(\theta_j)$, but does not know the true parameter vectors $\theta_j$, the undertaking faces parameter uncertainty. To assess the appropriateness of methods to model parameter uncertainty for risk capital calculation we consider a criterion introduced in the recent literature. According to this criterion, we demonstrate that, in general, appropriateness of a risk capital model for each subrisk does not imply appropriateness of the model on the aggregate level of the overall risk.\\ For the case where the overall risk is given by the sum of normally distributed subrisks we prove a theoretical result leading to an appropriate integrated risk capital model taking parameter uncertainty into account. Based on the theorem we develop a method improving the approximation of the required confidence level simultaneously for both - on the level of each subrisk as well as for the overall risk.

## Suggested Citation

• Andreas Frohlich & Annegret Weng, 2017. "Parameter uncertainty for integrated risk capital calculations based on normally distributed subrisks," Papers 1704.01608, arXiv.org.
• Handle: RePEc:arx:papers:1704.01608
as

File URL: http://arxiv.org/pdf/1704.01608
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## Citations

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Cited by:

1. Dina Manolache Aurora Elena, 2019. "Stress and scenario tests in the context of a Romanian non-life insurance company," Proceedings of the International Conference on Business Excellence, Sciendo, vol. 13(1), pages 149-161, May.

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