Section 8 - Tutorial R and In-Class Questions R

Question 1

Q4 An insurance company has recorded the claim numbers for four similar but distinct
policies over the past three years. The data table below shows the number of
claims 𝑌𝑖𝑗 for each policy 𝑖, 𝑖 = 1, 2, 3, 4 in year 𝑗, 𝑗 = 1, 2, 3.
𝑌𝑖1 𝑌𝑖2 𝑌𝑖3
𝑖 = 1 105 119 127
𝑖 = 2 125 136 141
𝑖 = 3 85 93 104
𝑖 = 4 94 103 121
Estimate 𝑌14, the number of claims for risk 1 in year 4 using EBCT Model 1.
The data is given on Canvas in “EBCT Q4 data.csv”.

Answer 1

ABC

Question 2

Q5 An insurance regulator is analysing the claim experience of three different
insurance companies selling similar products, using an Empirical Bayes Credibility
Theory approach.
The regulator has obtained the amounts of claim payments made and the number
of policies sold by each insurer over the past 4 years, as shown in the table below.
YEAR 1 YEAR 2 YEAR 3 YEAR 4
INSURER 1 £32.1m £35.7m £42.3m £39.1m
432 434 456 449
INSURER 2 £81.1m £85.6m £93.7m £91.2m
5524 5826 6241 6075
INSURER 3 £153m £161m £182m £176m
12,689 14,831 16,472 15,963
i) Use EBCT Model 1 to predict the total claim payment to be made by
Insurer 1 in the coming year. [9]
ii) Now use EBCT Model 2 to predict the total claim payment to be made
by Insurer 1 in the coming year, based on the expected number of
policies to be sold which is 460.
iii) Comment on your results. [3]
The data is given on Canvas in “EBCT Q5 claims data.csv” and “EBCT Q5 volume
data.csv”.

Answer 2

ABC