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CPS2051 Mentje G. et al.
1000 repeated GPD and Venter VaR estimates, i.e. [ (51) −
( 1 ,…, 1000 )
1, (951) − 1]. The results are given in Figure 1 overleaf. Note
( 1 ,…, 1000 )
that light grey represents the GPD band and dark grey the Venter band, while
the overlap between the two bands are even more dark.
Figure 1: VaR bands for different Burr parameter sets and frequency
combinations.
From Figure 1 we make the following observations:
For small frequencies ( ≤ 10) the GPD approach outperforms the Venter
approach, except for short tailed severity distributions and higher quantile
perturbations.
When the annual frequency is high ( ≥ 50) and for moderate to high
quantile perturbations ( ≥ 0.2) the Venter approach is superior, and more
so for higher and .
Even for small quantile perturbations ( = 0.1) and high annual frequencies
( ≥ 50) the Venter approach performs reasonable when compared to the
GPD. The above information suggest that provided enough loss data is
available, the Venter approach is the best choice.
4. Discussion and Conclusion
In this paper we motivated the use of Venter’s approach whereby the
severity distribution may be estimated using historical data and experts’
scenario assessments jointly. The way in which historical data and scenario
assessments are integrated incorporates measures of agreement between
these data sources, which can be used to evaluate the quality of both.
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