Company X has traditionally purchased public liability insurance from the ground up, but to decrease the insurance premium (currently at £2,500,000) spend and in view of its financial robustness, it is now investigating the opportunity of retaining the portion of each loss, which is below a given amount (‘each and every loss [EEL]

deductible’).

The company has obtained these two quotes for insurance at these different levels of deductibles:

a. EEL = £100k → Premium = £900,000

b. EEL = £200k → Premium = £450,000 The company asks a consultant what level of EEL they should choose, and the consultant proposes to choose the level of EEL that minimises the ‘total cost of risk’.

i. State the formula for the total cost of risk.

The company gives the consultant this further information:
• They are not worried about overall level of retained losses that happen with a probability of less than 1% (on an annual basis).
• The company’s CoC is 12%
ii. Explain what the CoC is.
An actuarial analysis gives the following estimates of the gross, retained and ceded distributions for different levels of EEL.
The company also asks the consultant to estimate what the premium will be if the EEL should be £500K. The consultant produces the following desk quote:
− EEL = £500k → Premium = £120,000

c. Explain what a desk quote is.

d. Based on the information provided, determine the best of the four options (no EEL, EEL = £100k, EEL = £200k, or EEL = £500k) from a total cost of risk’s perspective, explaining your reasoning.

e. Explain what the main uncertainties around this result are.