A medium-sized UK-based company (A) is currently insuring its public liability risks with an insurance company (B). You have been asked (as a consulting actuary) to advise company A on whether or not it is paying too much for its insurance.

The loss data (which is based on information provided on 30 September 2012) is in the following table. The year is the accident year. The loss data has been revalued with a claims inflation of 5% per annum to 1 July 2013. All losses are from the ground up and are expressed in British pounds.

2005 2006 2007 2008 2009 2010 64,995 56,284 7115 2237 4801 97,938 119,630 101,993 14,952 2060 159,535 85,959 1010 27,036 8576 25,106 55,957 259,414 2559 745,954 71,563 33,277 346,021 75,680 30,319 6582 2634 3297 59,881 104,119 536 81,287 Total 616,060 187,872 1,270,905 29,403 370,170 183,897

• Claims are typically reported within a year of occurrence.

• Some of the figures in the most recent years are reserved claims (estimates).

• The company turnover has changed little in the last 5 years and no changes are expected in the near future.

• The loss ratio for public liability in the UK market is between 70% and 90%.

• The current insurance policy is as follows:

i. EEL deductible = £100k.

ii. AAD = £2M.

iii. Individual/aggregate limit = £5M.

• The premium proposed by company B for 2013 is £300,000.

• The policy is annual and incepts on 1 January. It covers losses occurring during the policy year.

• Claims inflation is at 5% (already incorporated in the table above).

i. Describe how a commercial insurance policy with an EEL, AAD and individual/aggregate limit works and explain what it is trying to achieve. Build a simple numerical example with three losses that shows how EEL and AAD work. Make sure that the example is non-trivial (i.e. both the retained and the ceded amount are non-zero, and the AAD is hit).

ii. Using burning cost analysis, determine the expected losses ceded to the insurance programme for next year. State all the assumptions you have made.
iii. Based on the analysis in (ii) and on any additional considerations, estimate the technical premium and comment on whether the insurance is priced in line with market practice.
iv. Explain whether you think each of the values of EEL, AAD and individual/
aggregate limit are adequate. Suggest an alternative for any value(s) you consider inadequate and explain your reasoning. Explain qualitatively (or quantitatively where possible) how the changes you propose will affect the price of the policy.