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# 10 ans - MATH 471 Actuarial Theory I Homework#10 Fall 2010...

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MATH 471: Actuarial Theory I Homework #10: Fall 2010 Assigned November 3, due November 17 1. Consider a fully continuous whole life insurance of 1000 on (x). Assume δ = 0.08 and μ x ( t ) = 0.04 for t 0. (a) Find the annual benefit premium. (40) (b) Find the annual 20th percentile premium. (142.22) 2. For a fully continuous 5-payment 10-year endowment insurance of 1000 on (70): (i) Mortality follows de Moivre’s Law with ω = 105. (ii) δ = 0.1 (a) Provide the expression for the loss-at-issue random variable, L , where ¯ P denotes each premium. (b) Calculate the annual benefit premium. (120.58) 3. Each of 100 independent lives, all age 35, has mortality that follows l x = 100 - x for 0 x 100, and i = 6%. Let L j denote the loss-at-issue random variable for life j , where j = 1, 2, ..., 100. (a) Determine ¯ P ( ¯ A 35 ), and var ( L j ) (based on ¯ P ( ¯ A 35 )). (0.0203, 0.1187) (b) Let S denote the sum of all L j . Using the normal approximation, deter- mine the initial fund amount, h , that is necessary so that the insurer is 99% sure that S will not exceed h . (8.01) 4. On January 1, 2010, Pat purchases a fully continuous 5-payment 10-year

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10 ans - MATH 471 Actuarial Theory I Homework#10 Fall 2010...

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