Homework Assignment 19:
(1)
A continuoustime surplus process has a compound Poisson claims process.
(i)
The claim amount distribution is inverse Gaussian with
α
= 1.0 and
β
= 0.02.
(ii)
The relative security loading is positive.
(iii)
The adjustment coefficient does not exist.
Determine an upper bound for
ψ
(0).
(See Example 13.4.3 on page 412)
(Ans 0.291)
(2)
A continuoustime surplus process has a compound Poisson claims process with
λ
=12.
(i)
Claim amounts can be only 20,000 or 30,000, and these are equal in probability.
(ii)
Premiums are collected continuously at the rate of expected claims.
(iii)
There is no initial surplus.
(iv)
Ruin occurs if surplus drops below 0.
(a)
Calculate the probability of eventual ruin.
(Ans 1.00)
(b)
Given that ruin will occur, calculate the conditional expected value of the amount of the
first negative surplus. (Ans:
–13,000)
(3)
A continuoustime surplus process has a compound Poisson claims process.
(i)
The claim amount distribution is exponential with mean 2.
(ii)
The relative security loading is positive.
(iii)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 CharlesDann
 Probability theory, Exponential distribution, relative security loading, continuoustime surplus process

Click to edit the document details