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Unformatted text preview: MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Midterm #1 Additional Problems: Spring 2011 1. Consider a fully continuous whole life insurance on (x): (i) Annual effective interest rate i , and force of interest = ln(1 + i ). (ii) b t = (1 + r b ) t for t 0. (iii) t = (1 + r ) t for t 0. (a) Show: t V = (1 + r b ) t A b x + t- (1 + r ) t a x + t , where A b x + t uses b = - ln(1 + r b ), and a x + t uses = - ln(1 + r ). (b) Suppose this insurance is issued on (35) whose mortality follows de Moivres Law with = 100. Also: i = 6%, r b = 3%, r = 1%. Use (a) and the equivalence principle to calculate . (0.0315) (c) Using (a) and (b), calculate the terminal benefit reserve for the third year. (0.0521) 2. For a special fully discrete whole life insurance of 1000 on (75): (i) k = (1 . 05) k for k = 0, 1, ..., 29 (ii) Mortality follows de Moivres Law with = 105. (iii) i = 0.05 (iv) Premiums are calculated using the equivalence principle. Calculate: . (33.06) 3. For a special fully continuous whole life insurance on (x): (i) The death benefit at time t is b t = 1000 e . 03 t , t 0....
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This note was uploaded on 05/18/2011 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08