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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 decisionmaker is (globally) riskaverse 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 riskaverse 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 riskaverse 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 riskaverse individual would be willing to...
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