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A generalization of the $$q$$-exponential discounting function. (English) Zbl 1402.91131
Summary: The aim of this paper is to generalize the $$q$$-exponential discounting function introduced by D. O. Cajueiro [“A note on the relevance of the q-exponential function in the context of intertemporal choices”, Physica A 364, 385–388 (2006; doi:10.1016/j.physa.2005.08.056)] using the hyperbolic function as a base. The presented generalization has two aspects. First, we consider any discounting function $$F(t)$$, and not just hyperbolic discounting. Second, the value of the parameter $$q$$ is extended to the joint interval $$(- \infty, 1) \cup(1, + \infty)$$. In this way, we have found a family of discounting functions whose elements are subadditive or superadditive according to the value of $$q$$.

##### MSC:
 91B16 Utility theory 91B06 Decision theory 91B80 Applications of statistical and quantum mechanics to economics (econophysics)
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##### References:
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