Large Claims Modelling

Overview

For a given class of business we can (if we wish) split the model into attritional claims for that class (i.e. general "everyday" claims), large claims (occaisional very large individual claims, likely to be "a few" each year) and catastrophe claims (events giving rise to large aggregations of claims including perhaps some very large ones and also lots of smaller ones).

Attritional claims are often modelled by Loss Ratio simulations. Catastrophe claims may be modelled with the use of a specific catastrophe model. Large claims are often modelled using a frequency x severity model. For example the ICA working party in 2006 suggested that large claims will be modelled using a frequency * severity model calibrated to actual experience. Password is "ica2006".

Code

I've created a new page which shows the R code I've developed (comments welcome).

Frequency

First the number of large claims in a period (N) is sampled. This random variable is often chosen to be:

• Poisson or
• Negative Binomial.

Severity

For a given number of claims in the period "n" (a sample from N) we can then simulate the financial amount of the claim.

Given we are simulating large claims, typical distributions are:

• Pareto
• Lognormal?? Can someone tell me if this is used?
• Gamma

Correlation with attritional claims

It is possible (though not necessary) that in a year when there are more or less than average attritional claims that there will also be more or less large claims. This could be modelled by allowing the parameter of either (or both) the frequency and severity distribution for classes to depend on the loss ratio from attritional claims.

Correlation between classes

There are a number of ways we could correlate simulations between classes. We could produce a large number of simulations and then glue these together with a [www.copulas.pbwiki.com|copula]

An alternative method is to allow the parameter of either (or both) the frequency and severity distribution for classes to depend on a shared parameter which is itself random. These are so called mixture models.

Finally, if correlation with attritional claims is allowed for (as discussed above) and if correlation between attritional claims in different classes has been allowed for - then large claims will also be correlated as a consequence.

Proposed model

Where:

F_N = chosen Distribution for N

parameters = P(baseParameters, attritionalForClass, sharedParameters(class₁, class₂, ....class_m)

class_i = other classes that share a parameter with the chosen class.

Where:

F_S = chosen Distribution for S

parameters = P(baseParameters, attritionalForClass, sharedParameters(class₁, class₂, ....class_m)

Then for a given year the large losses are:

S₁, S₂ ... S_N

These will be returned as a vector - because the reinsurance module may need to know the seperate details of individual large claims.