A discount function is used in economic models to describe the weights placed on rewards received at different points in time. For example, if time is discrete and utility

Utility

In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....

 is time-separable, with the discount function
with defined as consumption at time t,

total utility is given by
.

Total utility in the continuous-time case is given by


provided that this integral exists.

Exponential discounting and hyperbolic discounting

Hyperbolic discounting

In behavioral economics, hyperbolic discounting is a time-inconsistent model of discounting.Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the...

are the two most commonly used examples.