Question: Suppose that a person has a given fortune A > 0 and can bet any amount b of this fortune in a certain game (0

Suppose that a person has a given fortune A > 0 and can bet any amount b of this fortune in a certain game (0 ≤ b ≤ A). If he wins the bet, then his fortune becomes A + b; if he loses the bet, then his fortune becomes A − b. In general, let X denote his fortune after he has won or lost. Assume that the probability of his winning is p (0 < p <1) and the probability of his losing is 1− p. Assume also that his utility function, as a function of his final fortune x, is U(x) = log x for x >0. If the person wishes to bet an amount b for which the expected utility of his fortune E[U(X)] will be a maximum, what amount b should he bet?

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For any given value of b EUX p logA b 1 p logA b Therefore EUXb pA b 1 pA b When this derivati... View full answer

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