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Problems with Cat Models
 Intensive calculations (Location x Event)
Cost to build, setup and run
Formulaic approach to largest events ignores mathematical tools
(We don’t have claims examiners directly establish ILF’s)
Many assumptions and estimates required: Curve forms, data
fits, extrapolations, interactions, ex post tests
Testing against real events forces answers to results that may
have been aberrations
Extreme Value Theory
For large events, for large number of samples from i.i.d’s, the
order statistic can’t be distinguished from a Generalized Pareto
Distribution (“GPD”).
| Lim |
Lim |
Max ( Abs ( Order Statistic^ -1 - GPD)) = 0 |
| Samples |
Size |
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Cat Models have two essential parts:
- Order Statistic ( The Xth %ile largest hurricane causes $D
in losses)
- Frequency Pattern (We expect T hurricanes per year)
So, we can use Extreme Value Theory to build a very different
kind of Cat Model.
Cat Models Without Physics
If:
- We have the GPD parameters for the industry size-of-loss distribution
for large losses from a Cat peril, and
- We have a description of the moments of the relationship between a
company’s loss and the industry’s (mean share, variance of share,
correlation between share and size of industry loss)
Can we find:
- The GPD parameters for the company size-of-loss distribution, and
- Return times for the company?
This is now just an algebra problem.
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