Five topics, weighted by the share of marks they carry. Stochastic processes and survival models are the largest, at 25% each.
Topic 1
Random variables and distributions for risk modelling, 20%
Topic 2
Time series, 20%
Topic 3
Stochastic processes, 25%
Topic 4
Survival models, 25%
Topic 5
Machine learning, 10%
What the topics cover
Questions can draw on any part of the syllabus in any session, so prepare across all of it.
Area
Syllabus objectives
Loss distributions and reinsurance
1.1
Compound distributions, copulas and extreme values
1.2 to 1.4
Time series models
2.1
Fitting and forecasting time series
2.2
Stochastic processes and Markov chains
3.1 and 3.2
Markov jump processes
3.3
Survival models
4.1
Estimating lifetime distributions and transition intensities
4.2 to 4.4
Graduation and mortality projection
4.5 and 4.6
Machine learning
5.1
Try a question
Pareto claims under excess of loss
Paper A style · Losses and reinsurance · Straightforward · 8 marks
Individual claim amounts on a household contents portfolio follow a Pareto distribution with parameters α=4 and λ=2,400, so that F(x)=1−(2400+x2400)4 for x>0. The insurer has an individual excess of loss reinsurance treaty with retention £2,000.
(i)
Calculate the probability that a claim involves the reinsurer, to 4 significant figures.
1 mark
(ii)
Calculate the insurer's expected payment per claim, to the nearest penny.
3 marks
(iii)
Calculate the reinsurer's expected payment on a claim that involves the reinsurer, to the nearest penny.
2 marks
(iv)
Hence calculate the reinsurer's expected payment per claim (including claims that do not involve it), to the nearest penny, and check your answers against the mean claim amount.