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What is the investor initial utility of wealth

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Suppose an investor with $2 in capital has a logarithmic utility of wealth function: . The investor has the opportunity to buy a gamble similar to that described in the St. Petersburg paradox. The gamble is the same as that described in the St Paradox except that the maximum number of coin tosses is set to 10. That is, the gamble ends and the payoff is $0 if a tails lands on the 10th coin toss. Moreover, let us define as the coin toss indicator. If heads lands on the th coin toss, the pay-off is $ and the gamble ends. If a tails lands on coin tosses one through to nine, the coin is tossed again.

What is the investor's initial utility of wealth? Report your response to four decimal places.

Reference no: EM132949260

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