Valuing the distant future under stochastic resettings: the effect on discounting

Abstract

We investigate the effects of resetting mechanisms when valuing the future in economic terms through the discount function. Discounting is specially significant in addressing environmental problems and in evaluating the sense of urgency to act today to prevent or mitigate future losses due to climate change effects and other disasters. Poissonian resetting events can be seen in this context as a way to intervene the market, it modifies the discount function and it can facilitate a specific climate policy. We here obtain the exact expression of the discount function in Laplace space and attain the expression of the long-run interest rate, a crucial value in environmental economics and climate policy. Both quantities are obtained without assuming any model for the evolution of the market. Model specific results are achieved for diffusion processes and in particular for the Ornstein-Uhlenbeck and Feller processes. The effect of Poissonian resetting events is non-trivial in these cases. The overall lesson we can learn from the obtained results is that effective policies to favor climate action should be resolute and frequent enough in time: the frequency of the interventions is critical for actually observing the desired consequences in the long-run interest rate.