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The Industry Size of Loss GPD
 Losses are positive valued
Assert that Cat losses are unbounded. (If you were king, how
much would you spend to avoid the “big one”?)
GPD can be expressed as the particular case of the Pareto:
The Company Size of Loss GPD
Theorem: Q ≤ q
Proof: If Q > q, then there are return times
when $Y > $X, which can’t be, since the
company is a subset of the industry.
The Share R.V.: S = $Y / $X
We need an assumption about the shape of the distribution of S,
given the level
of $X.
The easiest assumption is independence. (But other assumptions
can give direct solutions also.)
We will further assume that S is from a Beta distribution. This
is reasonable if we believe that the company’s exposures are:
- Not a single point
- Contiguous
- Continuously varying.
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