Lottery (probability)

In decision theory, the lottery is a theoretical construct in order to model the possibility of a risky future cash flows can.

General assumptions

It is often assumed that a subsequent payment to a decision depends on a state of the environment, which is still unknown at the time of the decision and can not be influenced by the decision maker. In general, however, one makes assumptions about the probability distribution of the amount of the payment.

The amount of the future payment can follow different distributions depending on the application. In the simplest case reaches a future payout, the high low and with a probability fails with a probability in order to shed light on theoretical issues such as risk aversion can.

Examples

A simple lottery is constructed by throwing a fair coin, pointing with probability 0.5 and with probability 0.5 head number. With head for example, 100 € will be paid, at number 0 €.

Also, the investment in shares can be considered as lottery. If the payment of the value of the stock at a specified future date, you go out usually by a log- normally distributed future payoff.

Notation

Formally describes a lottery with

Whereby cash and are the probabilities.

If the amount of the payments is not finite, then a lottery will be defined by means of a distribution function.