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Hyperbolic discounting is mathematically described as = + where g(D) is the discount factor that multiplies the value of the reward, D is the delay in the reward, and k is a parameter governing the degree of discounting (for example, the interest rate).
Time preferences are captured mathematically in the discount function. The main models of discounting include exponential, hyperbolic, and quasi hyperbolic. The higher the time preference, the higher the discount placed on returns receivable or costs payable in the future.
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 ...
The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic functions that does not involve complex numbers. The graph of the function a cosh( x / a ) is the catenary , the curve formed by a uniform flexible chain, hanging freely between two fixed points under uniform gravity.
Some formulations treat β not as a constant, but as a function β(t) that itself varies over time, for example in models which use the concept of hyperbolic discounting. This view is consistent with empirical observations that humans display inconsistent time preferences.
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Theory No. 3: Luka Dončić was a defensive liability. Believability: 2 out of 5 stars. The first quote to come out of Dallas’ camp was a telling one.