Question: Please write clearly, thank you! 3. (30 points] Consider the following gambling model. A person can bet any non-negative amount up to his present fortune.

Please write clearly, thank you!

3. (30 points] Consider the following gambling model. A person can bet any non-negative amount up to his present fortune. He will either lose that amount with probability 1 p, or win twice that amount with probability p. For example. if he bets 31, then he will win $2 with probability p and lose $1 with probability 1 p. A risk loving gambler has A dollars in hand and n chances to bet. His utility function is given by 1:.(35) = 3:2, where I is his nal fortune. Determine this person's optimal betting strategy. (Hint: Be sure to check the second-order condition.)

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