by Ivar Ekeland, Yiming Long & Qinglong Zhou
In economic theory, and in optimal control, it has been customary to discount future gains at a constant rate δ > 0 (…). That future gains should be discounted is well grounded in fact. On the one hand, humans prefer to enjoy goods sooner than later (and to suffer bads later than sooner), as every child-rearing parent knows. On the other hand, it is also a reflection of our own mortality: 10 years from now, I may simply no longer be around to enjoy whatever I have been promised. These are two good reasons why people are willing to pay a little bit extra to hasten the delivery date, or will require compensation for postponement, which is the essence of discounting. On the other hand, there is no reason why the discount rate should be constant, i.e. why the discount factor should be an exponential e−δt.