# Cumulative Prospect Theory

Cumulative prospect theory was introduced by Daniel Kahneman and Amos Tversky in 1992. This theory defines the economic model for descriptive decisions under risk. Cumulative prospect theory is a further development of the prospect theory.
The major difference of cumulative prospect theory from its original version is that the concept of weighting is introduced in the cumulative probability distribution function as it is done in the rank-dependent expected utility theory. Daniel Kahneman was awarded the Bank of Sweden Prize in Economic Sciences in the Memory of Alfred Nobel in the year of 2002.

Daniel Kahneman received the award for his outstanding contributions in the domain of behavioral economics and mainly for the development of Cumulative Prospect Theory (CPT).

The prime reflection of the cumulative prospect theory is that the investors seem to think of the possible outcomes that are relative to a certain reference point but not to the final status. This phenomenon is popularly known as framing effect.
The cumulative prospect theory also holds that the investors take different risk attitudes towards losses and gains. Another observation of the theory says that people generally tend to underweight average events and overweight extreme events.

Cumulative Prospect Theory deals with Expected Utility Theory where some modifications are done like: final wealth with payoffs relative is replaced with the reference point, utility function is replaced with a value function and cumulative probability is replaced with weighted cumulative probabilities.

The following formula gives the value of the probability measure p, for the subjective utility of a risky outcome

U (p) = ∫0 -∞ v(x) d/dx (w(F(x)))dx + ∫∞ 0 v(x) d/dx (-w(1- F(x))) dx

Here,

F(x) = ∫dp, integration ranging from -∞ to x.
v = value function
w = weighting function

This formula is the generalized form of the original formulation given by Tversky and Kahneman. This theory allows for the arbitrary outcomes but not only for the finitely distinct outcomes. The application of cumulative prospect theory is varied and the theory is used in numerous situations that seem to be inconsistent with the standard and common economic understanding.