Original loss curves

[jack123]

It is explained in chapter 15 that for property the distributions of X might vary by risk size, hence it is better to use Y = X/M when constructing loss curves.

What confuses me is that the derivation of the expected loss cost for a property layer (page 10) in terms of Y relies on the assumption that
E = E[X][E[N]

However E = sum(Xis from 1:N) which will only equal E[X]E[N] if the Xis are identically distributed. (Which will not be the case if X varies by risk size)

So we have a formula for loss cost in terms of Y, which is only valid if the Xis are identically distributed. This seems to defeat the purpose of using Y rather than X.

 

[jack123]

Apologies if the above post is unclear - the letter S disappeared on submission. It is supposed to say E(S) = E[X]E[N] and E(S) = E[sum(Xis from 1:N)]

 

[Katherine Young]

You're quite right of course Jack.

In fact, quite a lot of work has been done on the problem of whether Y is independent of the characteristics of each individual risk. (This sentence itself implicitly raises your point, that risks are not necessarily identically distributed.) Section 2.2 of Chapter 15 describes some of these problems.

Just as with any other model, a loss curve is a simplification of a real-world process. Perhaps the most important thing then is to understand the simplifying assumptions and question whether these hold in practice.

That is exactly what you have done, so well done!

 

[jack123]

Ok, thanks!