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Actsc363A1SolutionSet

# Actsc363A1SolutionSet - Actuarial Science 363 DE Solution...

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Actuarial Science 363 DE Solution Set Assignment #1 June 12 th 2009 1. An individual has a fractional power utility function whereby: u(w) = w 0.8 where "w" is wealth. She is offered a wager (bet) where there is a 30% probability of winning a sound system worth \$10,000 (plus the return of the wager) and a 70% probability of losing the wager. Her initial wealth is \$30,000. a) Show that this person is risk averse. u (w) = w^0.8 >0 if w>0 u’(w) = 0.8*w^(-0.2) >0 if w>0 u”(w)= -0.16w^(-1.2) <0 So we have decreasing marginal utility which indicates that the individual is risk averse. b) What is the maximum bet she will make? Let G be the amount of the wager. 1) No wager, wealth is 30,000 and expected utility position is u (30,000) = 30,000^0.8=3816.77891. (2) If winning a sound system worth \$10,000, then wealth is 40,000. (3) If losing the wager, then wealth is 30,000-G. Therefore, the expected utility position is: 0.3 *( 40,000^0.8)+0.7*[(30,000-G)^0.8] Then, we can get the equation: 0.3 *( 40,000^0.8)+0.7*[(30,000-G)^0.8] = 3816.77891 1441.349321 + 0.7*[(30,000-G)^0.8] = 3816.77891 (30,000-G)^0.8 = 3393.470841 30,000-G = 3393.470841 ^ 1.25 G = 4099.678665 Therefore, the maximum bet she will make is \$4099.678665.

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Actsc363A1SolutionSet - Actuarial Science 363 DE Solution...

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