Suppose you can make up to 5 bets in a sequence. At each bet you choose a stake amount 3, which can be any nonnegative value less or equal to your...

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J3. Suppose you can make up to 5 bets in a sequence. At each bet you choose a stake amount 3,which can be any nonnegative value less or equal to your current fortune. The bet returns 23 withprobability 0.55 and nothing with probability 0.45. Assume interest rates are zero, and your initialwealth is $100000. Your objective is to maximize the expected utility of your ﬁnal fortune (after 5bets). If you are a log—utility investor, determine the optimal policy and ﬁnd the maximal expectedutility.