Ann Oper Res (2010) 177: 9–19
DOI 10.1007/s10479-009-0606-4
Extreme events, discounting and stochastic optimization
Yuri Ermoliev · Tatiana Ermolieva · Guenther Fischer ·
Marek Makowski
Published online: 8 September 2009
© Springer Science+Business Media, LLC 2009
Abstract The paper analyzes the implications of extreme events on the proper choice of
discounting. Any discounting with constant or declining rates can be linked to random “stop-
ping time” events, which define the internal discount-related horizons of evaluations. Con-
versely, any stopping time induces a discounting, in particular, with the standard discount
rates. The expected duration of the stopping time horizon for discount rates obtained from
capital markets does not exceed a few decades and, as such, these rates may significantly
underestimate the net benefits of long-term decisions. The alternative undiscounted stop-
ping time criterion allows to induce social discounting focusing on arrival times of potential
extreme events rather then horizons of market interests. Induced discount rates are condi-
tional on the degree of social commitment to mitigate risk. In general, extreme events affect
these rates, which alter the optimal mitigation efforts that, in turn, change events. The use of
undiscounted stopping time criteria requires stochastic optimisation methods.
Keywords Extreme events · Stopping time · Catastrophic risks · Discounting ·
Investments · Stochastic optimisation
1 Introduction
The aim of this paper is to analyze the implications of extreme events (scenarios) on the
choice of discounting for long-term decisions. It argues the advantages of using undis-
counted random stopping time criteria which include the traditional discounted average
Y. Ermoliev (
) · T. Ermolieva · G. Fischer · M. Makowski
International Institute for Applied Systems Analysis, Schlossplatz 1, 2361 Laxenburg, Austria
e-mail: ermoliev@iiasa.ac.at
T. Ermolieva
e-mail: ermol@iiasa.ac.at
G. Fischer
e-mail: fisher@iiasa.ac.at
M. Makowski
e-mail: marek@iiasa.ac.at