Tutorial 6

# Tutorial 6 - FIN 3220A Actuarial Models I Tutorial 6 23...

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FIN 3220A Actuarial Models I Tutorial 6 23 November 2005 1. A level premium whole life insurance of 1, payable at the end of the year of death, is issued to (x). A premium of G is due at the beginning of each year, provided that (x) survives. You are given the following: (i) L = the insurer’s loss when G = P x (ii) L* = the insurer’s loss when G is chosen such that E[L*] = -0.2 (iii) Var(L) = 0.3 Calculate Var(L*). 2. The random variable L is the loss at issue for a fully continuous whole life insurance of 1 on (40). You are given: (i) δ = 0.02 (ii) mortality follows de Moivre’s law with l x = 100 – x __ (iii) 2 A x = 0.379 (iv) premiums are determined by the equivalence principle Calculate Var(L). 3. For a special fully discrete whole life insurance of 1000 issued on the life of (75), increasing premiums, Π k , are payable at time k, for k = 0,1,2…. You are given: (i) Π k = Π 0 (1 + i) k (ii) mortality follows de Moivre’s law with ω = 105 (iii) i = 0.05 (iv) premiums are calculated according to the equivalence principle. Calculate

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Tutorial 6 - FIN 3220A Actuarial Models I Tutorial 6 23...

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