Please explain how the answers are reached: Especially the tables.

Explain the difference between proportional and non$-$proportional reinsurance contracts.

Proportional reinsurance means that all losses are shared proportionally between the parties.

The sharing depends on the face value of the policy.

Non$-$proportional reinsurance means that the reinsurer bears the losses $($above the retention

limit of the primary$)$ up to a certain maximum and the remaining part of the losses is borne by

the primary insurer. The sharing depends on the loss size.

A primary insurer has a small portfolio of only two policies. Policy $1$ has a face value of $80,$ and

last year there were losses of $30$ and $60.$ Policy $2$ has a face value of $100,$ and last year there were

losses of $30$ and $90.$ All numbers are in thousand Dollars.

Determine for each loss, how much the primary insurer and how much the reinsurer

would pay in case of an

a$.$ Surplus Share Treaty with retention limit of $40$ and one line is ceded to the

reinsurer, or

b$.$ Excess of Loss Treaty with a retention limit of $40$ and reinsurance is offered up to

a maximum of $80.$

Explain what both reinsurance contracts have in common and what differentiates them

from another.

ad $1.$

a$.$ Surplus Share Treaty: The quota for reinsurance for the first policy is $(80-$

$40$ and for policy $2\frac{80-40}{100}=40\%.$ The indemnity payments follow

these proportions.

b$.$ XL: The parts of the losses that fall within the layer of the reinsurer are

transferred to the reinsurance company.