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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 3

Portfolio Management

3.1 Expected Utility Functions

3.1.1 Utility Functions

Suppose we have different investment opportunities to choose from. These investments may affect our future wealth. For example, the task is to allocate an initial capital among several risky assets to form an investment portfolio. Once we decide on such a risky investment, the future wealth becomes uncertain so it follows some probability distribution. The investment selection procedure can be reduced to the optimization of the probability distribution of the uncertain future wealth. If the outcomes from all alternatives were certain, then we would select the investment that produces the largest return. For the case with uncertain outcomes, we may be interested ...

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