Determine the optimal for investor, Risk Management

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The investor has constant wealth 1 and is offered to invest in shares of a project that either gains 3/2 or loses 1 with equal probabilities. Therefore, if the investor obtains shares of this project his wealth is 1+3 α/2 with probability 1/2 and 1- α with probability 1/2. The investor is an expected utility maximizer with utility index u(z) = ln z. What is the optimal for this investor? (α Must be between 0 and 1).

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