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# 1. Estimate the probability that your firm will have defaulted in the next 10 years.

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

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