Induced Discounting and Its Implications to Catastrophic Risk Management

The implication of risks for justifying long-term investment remains a controversial issue. For example, how can we justify mitigation efforts for a 200-year flood that may, in fact, occur in one year or in 300 years? Discount rates obtained from capital markets are linked to assets with lifespans of a few decades and, as such, may significantly underestimate the results of long-term mitigations. In this paper, we show that the explicit treatment of extreme catastrophic events and related uncertain time horizons and risks induce dynamically adjusted discount rates, conditional on the degree of social commitment to mitigate risk. In particular, the standard time geometric (exponential) discount factors are induced by an event with time horizons characterized by a "memoryless" geometric (exponential) probability distribution. A set of such events induces declining time inconsistent discount rates that are dominated by least probable extreme events. In general, risk affects discount rates, which alter the optimal mitigation efforts that in turn, change the risk. We show that the induced discount factors can be analyzed by solving stochastic optimization problems. Our simulation results indicate that the misperception of time inconsistency associated with induced discounting may dramatically effect - delay or provoke - the possibility of catastrophic collapse.

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