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Power utility function9/10/2023 ![]() After the axiomatization by von Neumann & Morgenstern ( 1944) of Daniel Bernoulli’s 1738 expected utility theory (reprinted in Bernoulli 1954), it soon became clear that a setup richer than a function with one subjective dimension defined over lifetime wealth would be needed to model real world behavior such as the coexistence of insurance uptake and lottery play (for an early discussion of these issues, see Vickrey 1945). ![]() It thus comes as no surprise that attitudes toward such risks and how to model them have received considerable attention in economics. We further investigate the extent to which the use of ill-suited functional forms to represent utility may result in violations of prospect theory, and whether such violations disappear when using logarithmic utility.Īlmost any important real world decision involves considerable levels of risk. We then show how a one-parameter logarithmic utility function fits such stake effects significantly better under prospect theory than the power or exponential functions mostly used when fitting prospect theory models. While we find people to be risk seeking for small outcomes, this turns to risk neutrality and later risk aversion as stakes increase. ![]() In two experiments, we show that risk preferences may change over outcomes. Another fourfold pattern of risk preferences over outcomes, postulated by Harry Markowitz in 1952, has received much less attention and is currently not integrated into prospect theory. People have been shown to be risk seeking for small probability gains and large probability losses, while being risk averse for large probability gains and small probability losses. ![]() One of the stylized facts underlying prospect theory is a fourfold pattern of risk preferences. ![]()
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