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Suppose you can make up to 4 bets in a sequence. At each bet you choose a stake amount s, which can be any nonnegative value less or equal to your current fortune. The bet returns 2s with probability 0.6 and nothing with probability 0.4. Assume interest rates are zero and your initial wealth is $100,000. Your objective is to maximize the expected utility of your final fortune (after 4 bets). If you are a log-utility investor, determine the optimal policy and find the maximal expected utility.

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Statistics and Probability, Statistics

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