QUESTION 3

You are asked to price a fully discrete 4-year term insurance policy for a policyholder aged x :

• The death benefit is 1000 payable at the end of the year of death.
• The gross annual premium is G payable for two years.

You have decided to use the following assumptions to price the policy:

• qx+k=0.05 for k0
• i=10%
• Annual expenses are 10% of each premium.
• Profit loading is equal to 5% of each premium.

(a) Determine G using the equivalence principle, including the profit loading.

[6 marks]

(b) Determine the gross premium reserve at time k=0,1,2,3,4 , including the profit loading.

Hint: Use the recursive formula.

[5 marks]

The regulator requires the insurer to hold 2 times the gross premium reserves you have calculated in (b).

(c) Explain the rationale of the regulators requirement and calculate the required gross premium reserves the insurer is to hold.

[3 marks]

(d) Calculate the profit vector Prk for k=0,1,2,3,4 .

[5 marks]

(e) Calculate the profit margin at a hurdle rate r=12% .

[6 marks]

[Total 25 marks]