Utility and Portfolio Choice

If this relation holds at all levels of wealth the

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Unformatted text preview: or all gambles with E (ε) = 0 and positive variance. If this relation holds at all levels of wealth, the utility function is globally risk averse RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 5 Main Results from Utility Theory • A decision-maker is (globally) risk-averse if and only if his utility function of wealth is strictly concave at the relevant (all) wealth levels • If a utility function is twice differentiable then it represents risk-averse choices, if and only if u ′′(W ) < 0 → Some people take as the definition of a utility function that it is a function that satisfies u ′(W ) > 0 and u ′′(W ) < 0 (and that it can order preferences) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 6 The Notion of Risk and Insurance Premium • To induce a risk-averse individual to undertake a fair gamble, a compensatory risk premium would have to be offered, making the package actuarially favorable • To avoid a present gamble a risk-averse individual would be willing to...
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