悬赏求解一道经济保险题目

Question 1.
(50 marks)

Your current wealth consists of your home worth £250,000 and savings of £200,000.
The savings are earning 3% per annum.
Your home building insurance has come for renewal. Your estimates of the possible losses on the value of your house during the one year period of the insurance are:

Value of the Loss (£)	Probability
0	0.95
10,000	0.01
20,000	0.01
80,000	0.03

Your insurance company quotes the following premiums for different level of insurance:

Amount of Insurance (£)	Premium (£)
40,000	30 + AVL1
60,000	27 + AVL2
80,000	24 + AVL3

Where AVL = actuarial value of loss to the insurer (means the expected loss to the insurer).


You expect neither to increase nor to decrease your savings during the coming year.
The house is not expected to increase in value over the next year.
Your utility for wealth as at the end of the period is ln(W) where W is the end of period wealth.

a)
What should you do? Should you renew the insurance for full value of the house, insure for £80,000, insure for £60,000, insure for £40,000or cancel it?
Explain.
Show all workings.
b)
Suppose you have £2,000,000 in savings.
Would you change your insurance decision?

Insurance covers the first £x of loss.
To make your work simpler assume that if any losses occur on the house that all such losses occur at the end of the year and that the premium is paid at the start of the year.