Induced Discounting and Risk Management

The goal of this paper is to specify and summarize new approaches to discounting proposed in our catastrophic risk management studies. The main issue is concerned with justification of investments, which may turn into benefits over long and uncertain time horizon. For example, how can we justify mitigation efforts for expected 300-year flood that can occur also next year. The discounting is supposed to impose time preferences to resolve this issue, but this view may be dramatically misleading. We show that any discounted infinite horizon sum of values can be equivalently replaced by undiscounted sum of the same values with random finite time horizon. The expected duration of this stopping time horizon for standard discount rates obtained from capital markets does not exceed a few decades and therefore such rates may significantly underestimate the net benefits of long-term decisions. The alternative undiscounted random stopping time criterion allows to induce social discounting focusing on arrival times of the main concern (stopping time) events rather than horizons of market interests. In general, induced discount rates are conditional on the degree of social commitment to mitigate risk. Random stopping time events affect these rates, which alter the optimal mitigation efforts that, in turn, change events. This endogeneity of the induced discounting restricts exact evaluations necessary for using traditional deterministic methods and it calls for stochastic optimisation methods. The paper provides insights in the nature of discounting that are critically important for developing robust long-term risk management strategies.