For a fully discrete whole life insurance on a life age x yo

For a fully discrete whole life insurance on a life age x, you are given:

d = 0.05

A_x = 0.4

²A_x = 0.2

The annual premium is 0.05 times the amount of insurance.

     L is the loss-at-issue random variable for a policy of amount 1.

Write an expression for L.

Calculate E[L].   (Ans –0.2)

Calculate Var(L).     (Ans 0.16)

A company sells 135 policies of amount 1 and 10 policies of amount 3. Use the normal approximation to calculate the probability that the present value at issue of the insurer’s total gain on these policies will exceed 45. (Ans 0.023)

Solution

A company sells 135 policies of amount 1 and 10 policies of amount 3. Use the normal approximation to calculate the probability that the present value at issue of the insurer’s total gain on these policies will exceed 45. (Ans 0.023)

miu = 1+3 / 135+10   = 0.0276

miu = 0.0276 * 145 = 4

SD = srqt ( 0.0276*145* 0.9724) = 1.97

P( x >45)

P( z > 45 - 4   / 1.97 ) = 20.81

P( z > 20.81) = 0.000005