A 3-year endowment insurance on (70) provides death benefits of 400 payable at the end of the year of death, if this occurs within 3 years, plus a pure endowment of 200 at age 73, if the insured is then alive. This is purchased by three level premiums of 40.
You are given that q70 = 0.2, q71 = 0.4, q72 = 0.5, and the interest rate is a constant 100%.
(a) Give the complete distributions for the random variable L, and the random variable 1L. Use the latter to find the reserve at time 1.
(b) What should the level premium be if the insurer wants the smallest premium such that the probability of a positive loss is less than 25%?