# Prospect Theory

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Prospect theory
Prospect theory was developed by Daniel Kahneman and Amos Tversky in 1979 as a psychologically realistic alternative to expected utility theory. It allows one to describe how people make choices in situations where they have to decide between alternatives that involve risk, e.g. in financial decisions. Starting from empirical evidence, the theory describes how individuals evaluate potential losses and gains. In the original formulation the term prospect referred to a lottery. The theory describes such decision processes as consisting of two stages, editing and evaluation. In the first, possible outcomes of the decision are ordered following some heuristic. In particular, people decide which outcomes they see as basically identical and they set a reference point and consider lower outcomes as losses and larger as gains. In the following evaluation phase, people behave as if they would compute a value (utility), based on the potential outcomes and their respective probabilities, and then choose the alternative having a higher utility.
The formula that Kahneman and Tversky assume for the evaluation phase is (in its simplest form) given by where are the potential outcomes and their respective probabilities. v is a so-called value function that assigns a value to an outcome. The value function (sketched in the Figure) which passes through the reference point is s-shaped and, as its asymmetry implies, given the same variation in absolute value, there is a bigger impact of losses than of gains (loss aversion). In contrast to Expected Utility Theory, it measures losses and gains, but not absolute wealth. The function w is called a probability weighting function and expresses that people tend to overreact to small probability events, but underreact to medium and large probabilities.
To see how Prospect Theory (PT) can be applied in an example, consider a decision about buying an insurance policy. Let us assume the probability of the insured risk is

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