UtilityTheory - Introdu¸c˜ ao ` a Teoria da Utilidade...

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Unformatted text preview: Introdu¸c˜ ao ` a Teoria da Utilidade Estat´ ıstica Empresarial Cl´ audia Neves Estat´ ıstica Empresarial (EE 2011) Introdu¸c˜ ao ` a Teoria da Utilidade 1 / 10 Introduction Utility Theory The utility theory lies at the heart of modern portfolio theory. Utility functions give us a way to measure investor’s preferences for wealth and the amount of risk they are willing to undertake in the hope of attaining greater wealth. This makes it possible to develop a theory of portfolio optimization. We develop the basic concepts of the theory through a series of simple examples. For the sake of exposition, our examples of possible investments are purely academic and thus deliberately simplified. While they are much too simple to be directly relevant for real-life applications, they lay the foundation upon which the more complicated relevant theories are developed. Estat´ ıstica Empresarial (EE 2011) Introdu¸c˜ ao ` a Teoria da Utilidade 2 / 10 Utility functions A utility function measures an investor’s relative preference for different levels of total wealth. Definition A utility function is a twice-differentiable function of wealth u ( ω ) defined for ω > 0 which has the properties of non-satiation (the first derivative u ( ω ) > 0) and risk aversion (the second derivative u 00 ( ω ) < 0). We shall assume that any such utility function satisfies the two critical properties of non-satiation and risk aversion: The non-satiation property states that utility increases with wealth, i.e., that more wealth is preferred to less wealth, and that the investor is never satiated – he never has so much wealth that getting more would not be at least a little bit desirable.would not be at least a little bit desirable....
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UtilityTheory - Introdu¸c˜ ao ` a Teoria da Utilidade...

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