As the consulting actuary for WWW, you have produced the following gross loss model for their public liability (PL) risks. The model is based on 1000 groundup losses (min = £150, max = £1,280,000) over the last 10 years (700 of which are fully paid losses, and 300 are reserve estimates), and is a negative binomial with rate = 10 and variance-to-mean ratio of 2, and a lognormal distribution with parameters

μ = 11 and σ = 1.6.

Gross losses Return period (years) Percentile Total loss Total number 1 in 2 50% 1,480,167 9 1 in 4 75% 2,650,608 13 1 in 5 80% 3,008,045 14 1 in 10 90% 4,360,384 16 1 in 20 95% 5,791,894 18 1 in 50 98% 8,585,541 21 1 in 100 99% 11,320,404 23 1 in 200 99.5% 13,967,817 25 1 in 500 99.8% 20,279,446 27 1 in 1000 99.9% 24,251,589 28 Mean 2,115,331 10.0 Std Dev 2,451,803 4.6 The risk manager wants to use this information to decide on an aggregate limit for a PL policy. They would like to purchase insurance to cover for events with a return period of 1 in 200 years (0.5% probability), and they are asking you what confidence you have in your ‘1 in 200’ estimate (£13.97M), given that you only had 100 data points to start with. Without actually doing any calculations,

a. Explain what types of uncertainty are at play here, and how you could go about estimating their effect.

b. Based on (a), comment on whether their concerns over the 1 in 200 estimate are exaggerated.

c. Describe two possible ways in which you could increase your confidence in the 99.5% figure, by using information from WWW only or by using external information.