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theory, cumulative probabilities are transformed, rather than the probabilities themselves. This leads to the aforementioned overweighting of extreme events which occur with small probability, rather than to an overweighting of all small probability events. The modification helps to avoid a violation
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with a value function that depends on relative payoff, and replacing cumulative probabilities with weighted cumulative probabilities. In the general case, this leads to the following formula for subjective utility of a risky outcome described by probability measure
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The main observation of CPT (and its predecessor prospect theory) is that people tend to think of possible outcomes usually relative to a certain reference point (often the status quo) rather than to the final status, a phenomenon which is called
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A typical value function in
Prospect Theory and Cumulative Prospect Theory. It assigns values to possible outcomes of a lottery. The value function is asymmetric and steeper for losses than gains indicating that losses outweigh gains.
95:). Finally, people tend to overweight extreme events, but underweight "average" events. The last point is in contrast to Prospect Theory which assumes that people overweight unlikely events, independently of their relative outcomes.
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Rieger, M., Wang, M. & Hens, T. (2017). Estimating
Cumulative Prospect Theory Parameters from an International Survey. Theory and Decision, 82, 4, 567-596.
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Cumulative prospect theory has been applied to a diverse range of situations which appear inconsistent with standard economic rationality, in particular the
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and makes the generalization to arbitrary outcome distributions easier. CPT is, therefore, an improvement over
Prospect Theory on theoretical grounds.
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A typical weighting function in
Cumulative Prospect Theory. It transforms objective cumulative probabilities into subjective cumulative probabilities.
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Parameters for cumulative prospect theory have been estimated for a large number of countries, demonstrating the broad validity of the theory.
327:{\displaystyle U(p):=\int _{-\infty }^{0}v(x){\frac {d}{dx}}(w(F(x)))\,dx+\int _{0}^{+\infty }v(x){\frac {d}{dx}}(-w(1-F(x)))\,dx,}
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Tversky, Amos; Kahneman, Daniel (1992). "Advances in prospect theory: Cumulative representation of uncertainty".
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theory but not applied to the probabilities of individual outcomes. In 2002, Daniel
Kahneman received the
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is that weighting is applied to the cumulative probability distribution function, as in
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by replacing final wealth with payoffs relative to the reference point, replacing the
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in 1992 (Tversky, Kahneman, 1992). It is a further development and variant of
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Bank of Sweden Prize in
Economic Sciences in Memory of Alfred Nobel
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is the value function (typical form shown in Figure 1),
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CPT incorporates these observations in a modification of
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The main modification to prospect theory is that, as in
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is the weighting function (as sketched in Figure 2) and
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494:and the
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