Consider a permanent disability model with three states: State 0: Healthy, State 1: Permanently disabled, State...

Consider a permanent disability model with three states: State 0: Healthy, State 1: Permanently disabled, State 2: Dead. The transition intensities are µ x (0,1) = 0.02, µ x (0,2) = 0.03 and µ x (1,2) = 0.05 and the force of interest δ = 0.05 For a person who is healthy at age 50, calculate the following:

a) The probability that he dies before he is (70).

b) If the insured gets a sum of 20,000 annually paid continuously for a maximum period of 5 years starting when he becomes disabled. Find the actuarial present value of this annuity.

c) If the insured has a death benefit of 100,000 paid the moment of death, regardless of the state preceding his death. Find the actuarial present value of this insurance.

d) Calculate the annual premium charged for the above two benefits, given that the premium is paid continuously provided that the insured is in healthy state.

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orchestra answered 1 year ago

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