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The utility of an event x occurring at future time t under utility function u, discounted back to the present (time 0) using discount factor β, is (). Since more distant events are less liked, 0 < β < 1.
In economics, 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 time-separable, with the discount function f(t) having a negative first derivative and with c t (or c(t) in continuous time) defined as consumption at time t, total utility from an infinite stream of ...
[2] [6] The "discount rate" is the rate at which the "discount" must grow as the delay in payment is extended. [7] This fact is directly tied into the time value of money and its calculations. [1] The present value of $1,000, 100 years into the future. Curves representing constant discount rates of 2%, 3%, 5%, and 7%
Annual effective discount rate, an alternative measure of interest rates to the standard Annual Percentage Rate; Bank rate, the rate of interest a central bank charges on its loans to commercial banks; Discount yield, a rate used in calculating cash flows; Fees and other charges associated with merchant accounts
Therefore, the preferences at t = 1 is preserved at t = 2; thus, the exponential discount function demonstrates dynamically consistent preferences over time. For its simplicity, the exponential discounting assumption is the most commonly used in economics. However, alternatives like hyperbolic discounting have more empirical support.
The accumulation function a(t) is a function defined in terms of time t expressing the ratio of the value at time t (future value) and the initial investment (present value). It is used in interest theory .
Calculating the discount rate: “Would you rather have $100 today or $110 in one month?” Your choice indicates your discount rate. If you choose $100 today, your discount rate is at least 10%. If you choose $110 in one month, your discount rate is less than 10%. Now how about “$100 today or $101 in one month?”
The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future cash flow x ~ i {\displaystyle {\tilde {x}}_{i}} by the stochastic factor m ~ {\displaystyle {\tilde {m}}} , and then taking the expectation. [ 1 ]