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Unformatted text preview: The Hong Kong Polytechnic University Department of Applied Mathematics Semester 2, 2009/2010 Assignment Two Hand in solutions to questions 1, 3, 4, 5, 6, 7 and 8 by 6:30pm 9 March. This is worth 2.5% towards your final course mark. Late submissions may not be marked, and if marked will receive reduced or zero credit. 1. (Rain insurance) Gavin Joness friend is planning to invest $1 million in a rock concert to be held 1 year from now. The friend figures that he will obtain $4 million revenue from his $1 million investment unless, my goodness, it rains. If it rains, he will lose his entire investment. There is a 40% chance that it will rain the day of the concert. Gavin suggests that he buy rain insurance. He can buy one unit of insurance for $.50, and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $4 million. (a) What is the expected rate of return on his investment if he buys u units of insurance? (The cost of insurance is in addition to his $1 million investment.) (b) What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of return? [ Hint: Before calculating a general expression for variance, think about a simple answer.]Before calculating a general expression for variance, think about a simple answer....
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This note was uploaded on 04/10/2010 for the course AMA 532 taught by Professor Prof.yang during the Fall '10 term at New School.
- Fall '10