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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 \(q\).

91B16 Utility theory
91B06 Decision theory
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
Full Text: DOI
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