An aggregate distribution is specified as
agg [label] [exposure] [limit]? sev [severity] [frequency]
sev are keywords
[label], [exposure], [limit]? etc.
are user inputs, and the limit clause is optional.
agg Auto 10 claims sev lognorm 10 cv 1.3 poisson
creates an aggregate with label Auto, an expected claim count of 10, severity sampled from an unlimited lognormal distribution with mean 10 and CV 1.3, and a Poisson frequency distribution. The layer is unlimited because the limit clause missing. The label must begin with a letter and contain just letters and numbers. It can't be a language keyword, e.g. agg, port, poisson, fixed
Exposure can be specified in three ways.
123 claim[s] 1000 loss 1000 premium at 0.7 [lr]?
The first gives the expected claim count; the
claims is optional.
The second gives the expected loss with claim counts derived from average severity.
The third gives premium and a loss ratio with counts again derived from severity.
lr is optional and just used for clarity.
Limit are entered as layer
xs attachment or layer
Here are four illustrative examples. The line must start with
agg (no tabs or spaces first) but
afterwards spacing within the spec is ignored and can be used to enhance readability.
The newline is needed.
agg Example1 10 claims 30 xs 0 sev lognorm 10 cv 3.0 fixed agg Example2 10 claims 100 xs 0 sev 100 * expon + 10 poisson agg Example3 1000 loss 90 x 10 sev gamma 10 cv 6.0 mixed gamma 0.3 agg Example4 1000 premium at 0.7 lr inf x 50 sev invgamma 20 cv 5.0 binomial 0.4
Here is what each example produces.
Example110 claims from the 30 x 0 layer of a lognormal severity with (unlimited) mean 10 and cv 3.0 and using a fixed claim count distribution (i.e. always exactly 10 claims).
Example210 claims from the 100 x 0 layer of an exponential severity with (unlimited) mean 100 shifted right by 10, and using a Poisson claim count distribution. The exponential has no shape parameters, it is just scaled. The mean refers to the unshifted distribution.
Example31000 expected loss from the 90 x 10 layer of a gamma severity with (unlimited) mean 10 and cv of 6.0 and using a gamma-mixed Poisson claim count distribution. The mixing distribution has a cv of 0.3 The claim count is derived from the limited severity.
Example4700 of expected loss (1000 premium times 70 percent loss ratio) from an unlimited excess 50 layer of a inverse gamma distribution with mean of 20 and cv of 5.0 using a binomial distribution with p=0.4. The n parameter for the binomial is derived from the required claim count.
The inverse Gaussian (
Sichel and other distributions are available as mixing distributions.
The Aggregate Manual provides more details.
Several aggregates can be combined into a portfolio. They are aggregated assuming independence between the components. Before you roll your eyes and dismiss everything bear in mind 1) a substantial amount of correlation between results is generated by premium correlation (the cycle) and not loss correlation; 2) cats are often genuinely uncorrelated, e.g. East coast wind and Japan quake; 3) using the more advanced features of the language you can share mixing distributions to proxy correlation. A portfolio is entered:
port MyPortfolio agg Example1 10 claims 30 xs 0 sev lognorm 10 cv 3.0 fixed agg Example2 10 claims 100 xs 0 sev 100 * expon + 10 poisson agg Example3 1000 loss 90 x 10 sev gamma 10 cv 6.0 mixed gamma 0.3 agg Example4 1000 premium at 0.7 lr inf x 50 sev invgamma 20 cv 5.0 binomial 0.4
port statement must begin a newline. The
statements must be indented with one TAB. Use four spaces in the control box for a TAB.
The code above can be cut and pasted into the text box below to create an example. Make sure you remove leading spaced before