#### Summary

In this LP we learn a bit more about risk, but also about uncertainty. We start by seeing again how risk is analysed using Morgenstern and von Neumann’s expected utility theory. We also learn about alternative approaches, such as the Friedman-Savage and Markowitz perspectives, but especially Daniel Kahneman’s prospect theory. We end our study of risk and uncertainty by learning how game theory can help when analysing uncertainty.#### Risk:

#### EUT and other approaches:

- Expected utility theory
- Alternative approaches
**Prospect theory**

#### Uncertainty:

Prospect theory belongs to behavioural economics and outstands as an alternative model to *expected utility theory*, as the *neoclassical* assumption of the rational agent is put into question. This theory was developed by *Nobel laureate* *Daniel Kahneman* and his collaborator Amos Tversky in their “Prospect Theory: An Analysis of Decision under Risk”, 1979. They used results they gathered both from their own empirical observations and from various experiments.

Individuals establish *preferences* depending on a certain situation and specific circumstances, rather than in absolute terms. This means that depending on their initial situation, agents will act one way or another. One of the outcomes of this reasoning leads to behavioural asymmetries between situations of potential loss or gain. Individuals, for example, are generally more adverse to losses than they are attracted to gains. An endowment effect has also been distinguished, as the compensation required by someone to give away a *good*, is larger than he would be willing to pay in order to acquire it.

Prospect theory postulates the existence of a value function *V* (Δ*w*) that depends on the deviation from a reference point (determined in terms of wealth), and a function ∏ (*p _{i}*) that turns the weighted

*probabilities*applied in decision-making. In this context A is preferred to

*B*if: ∑∏(

*p*)

_{A}*V*(Δ

*w*) > ∑∏(

_{A}*q*)

_{B}*V*(Δ

*w*)

_{B}Function ∏ (*p*) is defined on the interval [0, 1] transforms the probabilities into decision making weighted probabilities. It is a function characterized by being monotonically increasing that intersects the 45 degrees line near the origin, so that the weights in decision-making are smaller than the probabilities, except for the very low probabilities.

The value function *V* (Δ*w*), which is shown in the adjacent diagram, is dependent on changes in wealth relative to a reference situation, having a sigmoid-shape: being concave for gains (*risk aversion*) and convex for losses (*risk seeking*). It presents a discontinuity at the origin with a steeper slope for losses than for gains.

This theory helps understand why the same individual can be, at different situations, risk-avoiding or risk-seeking. It explains behaviours observed in the economy such as the disposition effector why the same person may buy both a lottery ticket and an insurance policy.