A generalization of the -exponential discounting function

The aim of this paper is to generalize the q -exponential discounting function introduced by Cajueiro (2006) [1] 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 ( − ∞ , 1 ) ∪ ( 1 , + ∞ ) . In this way, we have found a family of discounting functions whose elements are subadditive or superadditive according to the value of q .