12.2 Three Sources of Uncertainty
Coefficient of Variation: \(\phi = \dfrac{\sigma}{\mu}\)
\[\begin{equation} \phi^2 = \underbrace{\phi_{indep}^2}_{\text{Independent Risk}} + \underbrace{\phi_{internal}^2}_{\text{Internal Systemic Risk}} + \underbrace{\phi_{external}^2}_{\text{External Systemic Risk}} \tag{12.1} \end{equation}\]Definition 12.1 Systemic Risk
- Risks that can vary across valuation classes
Remark.
Qualitative approaches is recommended for systemic risk
- Need to make assumptions about the correlation of the different risks
12.2.1 Quantitative vs Qualitative Analysis
Limitation of quantitative analysis
Requires lots of data that we don’t have
Only captures historical risk
Does not capture risk that did not have an episode (of systemic risk) in the experience period
\(\therefore\) Need qualitative measures as well to examine the uncertainty
| Effective | Not effective |
|---|---|
| Independent risk | Internal systemic risk |
| Past episodes of external systemic risk | External systemic risk that has not yet occurred |
Good stochastic model will fit away past systemic episodes (e.g. high inflation) while we still want to hold a margin for the future
Outcome dependent significantly on actual episodes of risk, not all potential ones (for systemic risk that was not fitted away)
- Need to judge if episodes in data are representative going forward
Model is unlikely to pick up internal systemic risk from the actuarial valuation process