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You are required to write a report of approximately 3,000 words. You must
work individually and all submitted reports will be checked for plagiarism
using on-line tools.
Any literature used should be formally cited.
You are an actuarial student doing an internship in an actuarial firm. As
part of your project you have to estimate the probability that your firm will
default in the next 10 years. Assume the risk process of your insurance firm
is given by
R(t) = U + γt −
X
N(t)
i=1
Xi
,where U is your initial capital, γ is the premium rate, N(t) is a Poisson
process and Xi are the claims.
Assume your initial capital U is £5000000, claims arrive at an average rate
of λ = 100 per year, and individual claims have mean £1
0000 and standard
deviation £100, and are distributed according to a Γ distribution. At the
moment your firm receives £500000 in premiums every year.
1. Estimate the probability that your firm will have defaulted in the next
10 years.
2. What should γ be to make sure the probability of default in the next
10 years is less than .5%?
Write a report to the principle actuary detailing the methods used in your
model and your findings.
