Project #73340 - decision-theoretic analysis of the alternating st petersburg lottery

1250 words with graphs... For the purpose of this research essay, the alternating St. Petersburg lottery is the following gamble. You toss a fair coin several times until heads come up for the first time. You receive $2 if heads come up on the first coin toss. You have to pay $4 if heads come up for the first time on the second coin toss (i.e., tails come up on the first coin toss but then heads come up on the second coin toss). You receive $8 if heads come up for the first time on the third coin toss. (i.e., tails come up on the first and second coin toss but then heads come up on the third coin toss). You have to pay $16 if heads come up for the first time on the fourth coin toss (i.e., tails come up on the first, second and third coin toss but then heads come up on the fourth coin toss). You receive $32 if heads come up for the first time on the fifth coin toss and so on. In other words, you receive (-1)n+1 * 2' dollars if heads come up for the first time on the n-th coin toss (with a usual convention that you receive positive dollar amounts but must pay negative dollar amounts). A good research essay should address the following points (up to a maximum of 30 points): A) Calculate the expected value of the alternating St. Petersburg lottery in form of an infinite series (5 points); B) Discuss the properties of this series; does it converge to a finite expected value? (5 points); C) Using your practical understanding of choice under risk and uncertainty, discuss what would be it reasonable value of the alternating St. Petersburg lottery; how much are you willing to pay in order to play such a lottery? (5 points); D) Using your theoretical understanding of choice under risk and uncertainty, discuss how such reasonable value can be rationalized/explained; for example, you may calculate the expected utility of the alternating St. Petersburg lottery with a specific concave utility function (15 points)

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Due By (Pacific Time) 06/11/2015 08:00 pm
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