RelativeResourceManager10

# RelativeResourceManager10 - l x = 100-x for 0 ≤ x ≤ 100...

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MATH 471: Actuarial Theory I Homework #10: Fall 2009 Assigned November 4, due November 18 1. Consider a fully continuous whole life insurance of 1000 on (x). Assume δ t = 0.06 and μ x ( t ) = 0.03 for t 0. (a) Provide the expression for the loss-at-issue random variable, L , where ¯ P denotes each premium. (b) Find the annual beneﬁt premium. (30) (c) Find the annual percentile premium so Pr ( L > 0) = 0.20. (106.67) 2. For a fully continuous 5-payment 10-year endowment insurance on (70): (i) The beneﬁt is 1000. (ii) Mortality follows de Moivre’s Law. (iii) ˚ e 70 = 17.5 and δ = 0.1 (a) Provide the expression for the loss-at-issue random variable, L , where ¯ P denotes each premium. Note: There are three diﬀerent ranges of T. (b) Calculate the annual beneﬁt premium. (120.58) 3. Each of 100 independent lives, all age 35, has mortality that follows

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Unformatted text preview: 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 ). (0.0203, 0.1187) (b) Let S denote the sum of all L j . Using the normal approximation, deter-mine what size fund, say h , is necessary so that the insurer is 90% sure that S will not exceed h . (4.42) 4. On January 1, 2010, Pat, age 40, purchases a fully continuous 5-payment 10-year term insurance of 100,000. Premiums of 4000 are payable continu-ously each year for the ﬁrst 5 years, and δ = 0.05. Calculate the value of L if Pat dies on June 30, 2012. (78,849.44)...
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RelativeResourceManager10 - l x = 100-x for 0 ≤ x ≤ 100...

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