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 is timeseparable, with the discount function having a negative first derivative and with (or in continuous time) defined as consumption at time t, total utility from an infinite stream of consumption is given by
 .
Total utility in the continuoustime case is given by
provided that this integral exists.
Exponential discounting and hyperbolic discounting are the two most commonly used examples.
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Bootstrapping a discount function

FRM Part I: Prices, Discount Factors, and Arbitrage Part I(of 2)

Discount rate basics
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See also
References
 Shane Frederick & George Loewenstein & Ted O'Donoghue, 2002. "Time Discounting and Time Preference: A Critical Review," ;;Journal of Economic Literature;;, vol. 40(2), pages 351401, June.