You are asked to help your underwriter with an actuarial quote for an aviation liability policy. Your actuarial model produces yearly expected losses of £1.2M.

To produce an estimate of the technical premium, you use the Cost Plus methodology. You want to take these elements into account: expenses, investment income, and profit.
You have the following additional information:

a. The weighted payment time of the claims is 6 years

b. Current gilt yields (as found, for example, on the FT) are as follows: 0.22%
(1 year), 0.91% (5 years), 1.43% (7 years), and 2.07% (10 years)

c. The target expense ratio (expenses/premium) is 28%

d. 10% of the premium is supposed to be for profit

e. No reinsurance will be purchased

f. The commission can also be ignored i. Based on the information above, write down a formula for calculating the technical premium explaining all its terms, and use it to estimate the technical premium After seeing your calculations, the underwriter is considering whether to buy excess-of-loss reinsurance in excess of £2M, and they ask you to estimate the losses that are expected to be ceded to the reinsurer as a result of that. You estimate that the expected losses in excess of £2M are going to be around £550k. In the meantime, the underwriter gets a quote from the reinsurer of £800k to cover that risk ii. Calculate the net reinsurance cost of the arrangement, and determine how the technical premium changes as a result of that iii. Explain why the technical premium might ultimately be different from the actual premium charged