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Power utility certainty equivalent1/1/2024 ![]() Formally, exponential utility is given by: In economics and finance, exponential utility is a specific form of the utility function, used in some contexts because of its convenience when risk (sometimes referred to as uncertainty) is present, in which case expected utility is maximized. Of particular interest are studies suggesting that a potassium test may possibly predict the response of IC patients to treatment with pentosan polysulfate.Exponential Utility Function for different risk profiles The results indicate that treatment should be continued for 6 months or longer in order to show significant improvement. Importantly, two longer-term, patient-evaluation studies showed that a longer duration of treatment with pentosan polysulfate resulted in greater improvements in patients' response rates and outcomes. of four randomized, prospective trials improved significantly in most variables with treatment by oral pentosan polysulfate in the two other studies, the IC patients improved in some domains with pentosan therapy, although not significantly. In randomized, double-blind studies, patient and investigator evaluations of pentosan polysulfate in the treatment of IC resulted in favorable assessments of the drug. Studies of the mechanisms and causes of interstitial cystitis (IC) and of the properties of pentosan polysulfate have provided a scientific rationale for using pentosan polysulfate to treat IC. It gives rise to different evaluations of gains and losses, which are not distinguished in the standard cumulative model, and it provides a unified treatment of both risk and uncertainty. The resulting model, called cumulative prospect theory, combines some of the attractive features of both developments (see also Luce and Fishburn J Risk Uncertain 4:29–59, 1991). This article presents a new version of prospect theory that incorporates the cumulative functional and extends the theory to uncertain as well to risky prospects with any number of outcomes. In an important later development, several authors (Quiggin J Econ Behav Organ 3, 323–343 Schmeidler Econometrica 57:571–587, 1989 Yaari Econometrica 55:95–115, 1987 Weymark Math Soc Sci 1:409–430, 1981) have advanced a new representation, called the rank-dependent or the cumulative functional, that transforms cumulative rather than individual probabilities. The key elements of this theory are (1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains, and (2) a nonlinear transformation of the probability scale, which overweights small probabilities and underweights moderate and high probabilities. Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky Econometrica 47:263–291, 1979 Tversky and Kahneman J Bus 59(4):S251–S278, 1986). The Johns Hopkins University Press, Baltimore, 1988 Machina Econ Perspect 1(1):121–154, 1987). Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer J Risk Uncertain 2:61–104, 1989 Fishburn Nonlinear preference and utility theory. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years.
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