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Hyperbolic discounting is an alternative mathematical model that agrees more closely with these findings. [5] According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days).
The point at which you forego the money is the social discount rate. Generally, this type of discounting resembles a hyperbolic curve as well. Probability discounting takes the same form, but with risk. Say you were offered a certain $50 or a $100 with a 50% chance of winning it. How about a 60% chance? Probability discounting is likewise ...
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 theory emphasizes time as a critical and motivational factor. The argument for a broad, integrative theory stems from the absence of a single theory that can address motivation in its entirety. Thus, it incorporates primary aspects of multiple major theories, including expectancy theory , hyperbolic discounting , need theory and cumulative ...
He explained this in terms of hyperbolic discounting of future rewards, derived from ideas that Rachlin and others had developed from Richard Herrnstein's matching law. Ainslie then integrated these ideas with earlier experimental and theoretical work on inter-temporal choice, for example the studies of Walter Mischel on delay of gratification ...
where E is the expectation operator, u is a known utility function (which applies both to consumption and to the terminal wealth, or bequest, W T), ε parameterizes the desired level of bequest, ρ is the subjective discount rate, and is a constant which expresses the investor's risk aversion: the higher the gamma, the more reluctance to own ...
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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 .