RelativeResourceManager5 - . 05 t ] (ii) = 0.01 (iii) =...

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MATH 471: Actuarial Theory I Homework #5: Fall 2009 Assigned September 23, due October 7 1. Suppose mortality follows l x = 110 - x for 0 x 110 and i = 0.08. (a) Calculate ¯ A 1 25: 30 . (0.1377) (b) Calculate var ( Z ), where Z is the present value random variable for a 30-year term insurance issued to (25) that pays 1 at the moment of death. (0.0567) 2. Assume μ x + t = μ and δ t = δ for t 0. Show that: ¯ A x = μ μ + δ . [Note: Memorize this result!!!] 3. Let Z be the present value random variable for a special continuous whole life insurance issued to (x), where for t 0: (i) b t = 1000 exp[0
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Unformatted text preview: . 05 t ] (ii) = 0.01 (iii) = 0.06 (a) Calculate the actuarial present value of this insurance. (500) (b) Calculate the variance of Z . (83,333.33) 4. Let Z be the present value random variable for a continuous 20-year term 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 < = 2 3 for 0 z < e-1 = 1 + ln( z ) 3 for e-1 z < 1 = 1 for z 1...
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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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RelativeResourceManager5 - . 05 t ] (ii) = 0.01 (iii) =...

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