RESUMO
We address the process of discounting in random environments, which allows valuation of the future in economic terms. We review several approaches to the problem regarding different well-established stochastic market dynamics in the continuous-time context and include the Feynman-Kac approach. We also review the relation between bond-pricing theory and discounting and introduce both the market price of risk and the risk neutral measure from an intuitive point of view devoid of excessive formalism. We provide the discount for each economic model and discuss their key results. We finally present a summary of our previous empirical studies for several countries on the long-run discount problem.
RESUMO
We analyze how to value future costs and benefits when they must be discounted relative to the present. We introduce the subject for the nonspecialist and take into account the randomness of the economic evolution by studying the discount function of three widely used processes for the dynamics of interest rates: Ornstein-Uhlenbeck, Feller, and log-normal. Besides obtaining exact expressions for the discount function and simple asymptotic approximations, we show that historical average interest rates overestimate long-run discount rates and that this effect can be large. In other words, long-run discount rates should be substantially less than the average rate observed in the past, otherwise any cost-benefit calculation would be biased in favor of the present and against interventions that may protect the future.