RelativeResourceManager6 - = 100, and = 0.06 (ii) h is the...

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MATH 471: Actuarial Theory I Homework #6: Fall 2009 Assigned October 7, due October 14 1. A continuous 15-year endowment insurance of 10,000 is issued to (x). Assume μ = 0.02 and δ = 0.05. (a) Calculate the actuarial present value of this insurance. (5356.70) (b) Calculate the standard deviation of the present value of the benefits. (1321.88) 2. For a continuous whole life insurance of 1 on (x): (i) δ t = 0.04 for 0 < t 10, δ t = 0.06 for 10 < t (ii) μ x ( t ) = 0.06 for 0 < t 10, μ x ( t ) = 0.08 for 10 < t Calculate the net single premium for this insurance. (0.5895) 3. Each of 100 independent lives age 30 purchase a single-premium 5-year deferred whole life insurance of 10 payable at the moment of death, where: (i) Mortality follows de Moivre’s Law with
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Unformatted text preview: = 100, and = 0.06 (ii) h is the aggregate amount the insurer receives from the 100 lives. Using the normal approximation, calculate h such that the probability the insurer has sucient funds to pay all claims is 0.95. (203.78) 4. Let Z be the present value random variable for a continuous 20-year endowment insurance of 1 on (40). Assume mortality follows de Moivres Law with limiting age 100, and = 0.05. Show that the cdf of Z , F Z ( z ), is such that: F Z ( z ) = 0 for z < e-1 = 1 + ln( z ) 3 for e-1 z < 1 = 1 for z 1 5. If u x ( t ) = and t = for all t > 0, show that: ( I A ) x = ( + ) 2 ....
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This note was uploaded on 02/14/2011 for the course MATH 471 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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RelativeResourceManager6 - = 100, and = 0.06 (ii) h is the...

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