Examples of what a user might want to do.

Used in defining the functional specification.

Use case 1

This is a model for a simple line of business. There are two claim types; attritional and large claims.

*Premiums are 10,000,000

*Attritional loss ratio is modelled as a gamma distribution with mean 70% and standard deviation 10%

*Attritional claims is defined as the attritional loss ratio * the premium

*The number of large claims is a Poisson random variable with Mean 0.8

*Each large claim is modelled as a generalised Pareto distribution with Threshold 250,000 Scale 500,000 and shape 0.2.

*Large claims is the total of any large claims.

*It is believed that there is a correlation of 0.3 between the total of the large claims and the total of the attritional claims.

*Total claims is the sum of Large claims and attritional claims

*Profit is the premiums less the total claims.

We think that running 10,000 trials should give us sufficient data. As outputs we are interested in the distibution of this profit function, but in particular the worst 0.5% result. (i.e. what is the loss in the 50th worst simulation). This result is known as the capital amount.

Use case 2

As use case 1 except we now have reinsurance.

*We can now make reinsurance recoveries if an individual large claim is above 500,000. We can recover the next 1,000,000 on that claim. The maximum amount we can recover across all such claims is 2,000,000.

*Profit is now Premiums less claims plus reinsurance recoveries

In addition to the profit function we are now also interested in the distribution and the mean reinsurance recoveries. We would also be interested in the capital both before and after the reinsurance.

Ideas for future use cases

• multiple lines of business
• payment patterns and cash flow
• Investment return and related risk