7 ans - MATH 471 Actuarial Theory I Homework#7 Fall 2010...

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Unformatted text preview: MATH 471: Actuarial Theory I Homework #7: Fall 2010 Assigned October 13, due October 20 1. Consider a 15-year endowment insurance of 10,000 on (30) with death benefit payable at the end of the year of death. Assume mortality follows de Moivre’s Law with ω = 90, and i = 0.05. (a) Calculate the actuarial present value of this insurance. (5337.57) (b) Calculate the standard deviation of Z , where Z is the present value random variable for this insurance. (1166.85) 2. For a special 3-year term insurance on (x): (i) Z is the present value random variable for the death benefits. (ii) q x + k = 0.02( k + 1) for k = 0, 1, 2 (iii) b k +1 = 300,000 + 50,000 k for k = 0, 1, 2 (iv) i = 0.06 Calculate: E ( Z ). (36,829.06) 3. A special term insurance policy pays 1000 at the end of the year of death for the first ten years and 2000 at the end of the year of death for the next 10 years. Mortality follows the Illustrative Life Table, and i = 0.06....
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7 ans - MATH 471 Actuarial Theory I Homework#7 Fall 2010...

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