first loss

[NeedToQualify]

Hi,

Does anybody know how a product can be priced if it is to be sold under a "first loss" basis? That is, the principle of average will not apply in cases of underinsurance. A common case is when insurers place a max value on the amount of cash that can be claimed under a household fire policy.

for example:
a household buildings product sold for a SI of 10,000 when the actual SI of policies could be more than 10,000.

How would you price something like this?
I think that this product will have the same frequency as the standard policy but the severity will be capped.

i.e. in the data each claim will be capped to 10,000.

Frequency= number of claims/ total exposure of data
Severity= total (capped) claim amounts/number of claims

premium rate (per actual SI)=frequency x (capped) severity

Premium= premium rate x actual SI

HOWEVER, when this product is sold you don't know the actual SI.

So I think the actual SI should be replaced by the average expected SI of the new business portfolio.

Any thoughts?

 

[Ian Senator]

Well, I've never priced one....but....

I'd have thought it best to stochastically model the severity so that you can incorporate the cap (or use integation with a limited expected value - easily obtained from first loss curves or ILFs).

Then how you express the premium rate would be up to you. So if you wanted to charge a rate per mille actual SI, you'd have to have a notional actual SI (must be reasonable to estimate this?). Or you could charge a higher rate per mille 'capped' SI. But surely either way you need to know/estimate the 'actual' SI otherwise you'd never know the true exposure?

Perhaps someone who has worked with such a line of business could enlighten us...

 

[NeedToQualify]

Thanks for the reply.

The stochastic approach seems interesting. If I understand correctly, a distribution would be fitted to the severity and then this distribution would be truncated thus changing both the shape and parameters of the distribution.

So, instead of going through each loss and truncating it, the new mean could be assessed by calculating the mean of the truncated distribution with suitable assumptions for the type of distribution.

Another question is that it seems appropriate to split buildings data into SI bands for pricing. This is because the year-on-year average cost per claim would be different depending on the mix of SIs. Is this correct?