2.4.9. The Reinsurance Clauses

Prerequisites: Excess of loss reinsurance terminology.

Occurrence and aggregate reinsurance can be specified in a way similar to limits and deductibles. Both clauses are optional. The ceded or net position can be output. Layers can be stacked and can include co-participations.

The options for both clauses are:

• Keywords ceded to or net of determine which losses flow out of the reinsurance.

• A fraction po limit xs attachment describes a partial placement, e.g., 0.5 so 3 xs 2.

• A participation so limit xs attachment describes a partial placement by the ceded limit, e.g., 1 po 3 xs 2. This syntax is equivalent to 0.333 so 3 xs 2.

An unlimited cover is denoted inf. Shares of unlimited covers must be expressed as shares, for obvious reasons.

Layers can be stacked using the and keyword. The initial net of or ceded to applies to all layers in the tower.

The occurrence reinsurance clause comes after severity but before frequency, because you need to know severity but not frequency. The aggregate clause comes after frequency. If frequency is specified using dfreq the occurrence clause comes before the aggregate clause.

The syntax is best illustrated with some examples.

Examples.

1. Occurrence reinsurance:

   agg Trucking                    \
   5000 loss 1000 xs 0             \
   sev lognorm 50 cv 1.75          \
   occurrence net of 750 xs 250    \
   poisson
   

specifies the distribution of losses to the net position on the Trucking policy after a per occurrence cession of the 750 xs 250 layer. This net position can also be written using limits and attachments rather than reinsurance:

agg Trucking                    \
?? loss                         \
250 xs 0                        \
sev lognorm 50 1.75             \
poisson

for some level of losses. Running:

agg Trucking                    \
5000 loss 1000 xs 0             \
sev lognorm 50 cv 1.75          \
occurrence ceded to 750 xs 250  \
poisson

models ceded losses.

2. Aggregate reinsurance:

   agg WorkComp                    \
   15000 loss                      \
   500 xs 0                        \
   sev lognorm 50 cv 1.75          \
   poisson                         \
   aggregate ceded to 50% so 2000 xs 15000
   

specifies the distribution of losses ceded to an aggregate protection for the 2000 xs 15000 layer of total losses (attaching at the loss pick), with occurrences limited to 500. The underlying business could be an SIR on a large account Workers Compensation policy, and the aggregate is a part of the insurance charge (Table L, M).

3. Occurrence and aggregate reinsurance:

   agg Trucking 5000               \
   loss 1000 xs 0                  \
   sev lognorm 50 cv 1.75          \
   occurrence net of 50% so 250 xs 250 and 500 xs 500  \
   poisson                         \
   aggregate net of 250 po 1000 xs 4000 and 5000 xs 5000
   

applies two occurrence and two aggregate layers to the Trucking portfolio. The 250 xs 250 occurrence layer is only 50% placed (so stands for share of), and the second is 100% (by default) of 500 xs 500. The net of the occurrence programs flows through to aggregate layers, 250 part of 1000 xs 4000 (25% placement, po stands for part of), and 100% share of the 5000 xs 5000 aggregate layers. The modeled outcome is net of all four layers. In this case, it is not possible to write the net of occurrence using limits and attachments.

Note

All occurrence reinsurance assumes free and unlimited reinstatements.

2.4.9.1. Layering Losses in a Tower

Underwriters are often interested in layering out losses from ground-up to the policy limit. For example, a 5M limit may be layered as 250 xs 0, 250 xs 250, 500 xs 500, 1000 xs 1000, and 3000 xs 2000. A tower can be input manually:

occurrence ceded to 250 xs 0 and 250 xs 250 and 500 xs 500  \
and 1000 xs 1000 and 3000 xs 2000

There is also a shorthand for layering, since it is quite common. A layering can be entered by specifying just the layer break points using the tower keyword:

occurrence ceded to tower [0 250 500 1000 2000 5000]

The tower does not have to start at 0 and does not have to exhaust the entire policy limit. Towers can be applied to occurrence and aggregate reinsurance.

See reinsurance pricing for more examples, including an approach to reinstatements.