Write separately the probabilities that Lydia’s insurance company will have to:
(i) Payout at the end of the first year of a policy.
(ii) Payout at the end of the second year of a policy.
(iii) Not have to pay out a policy at all.
b. Draw a detailed contingent cash flow diagram that models this income protection policy from the perspective of Lydia’s insurance company.
c. Calculate the premium $P that Lydia’s insurance company should charge for this income protection policy.
Lydia works for an insurance company. Her company wishes to provide an income protection policy to employed persons, which will provide the policyholders with a single payout of $10 000 in the event that they become unemployed within the next two years.
The premium $P for this policy would be paid at the beginning of the two-year period, and the payout, if required, would occur at the end of whichever one-year period during the policy that the policyholder became unemployed. Lydia’s insurance company would have to pay administrative costs of $60 at the start of the policy.
The interest rate is j1 = 9%. Suppose government statistics indicate the probability an employed person becomes unemployed within any one-year period is 1%. Further, suppose that Lydia’s insurance company wishes to earn on average a net 0.05P profit per policy (where P is the premium of the policy) as measured at the end of the two years.
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