Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model

CentER Discussion Paper Series No. 2010-122

42 Pages Posted: 5 Dec 2010

See all articles by Masako Ikefuji

Masako Ikefuji

University of Tsukuba

Roger J. A. Laeven

University of Amsterdam - Department of Quantitative Economics (KE)

Chris Muris

affiliation not provided to SSRN

J.R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics

Date Written: November 26, 2010

Abstract

In the context of extreme climate change, we ask how to conduct expected utility analysis in the presence of catastrophic risks. Economists typically model decision making under risk and uncertainty by expected utility with constant relative risk aversion (power utility); statisticians typically model economic catastrophes by probability distributions with heavy tails. Unfortunately, the expected utility framework is fragile with respect to heavy-tailed distributional assumptions. We specify a stochastic economy-climate model with power utility and explicitly demonstrate this fragility. We derive necessary and sufficient compatibility conditions on the utility function to avoid fragility and solve our stochastic economy-climate model for two examples of such compatible utility functions. We further develop and implement a procedure to learn the input parameters of our model and show that the model thus specified produces quite robust optimal policies. The numerical results indicate that higher levels of uncertainty (heavier tails) lead to less abatement and consumption, and to more investment, but this effect is not unlimited.

Keywords: Economy-climate models, Catastrophe, Expected utility, Heavy tails, Power utility

JEL Classification: D81, Q5

Suggested Citation

Ikefuji, Masako and Laeven, Roger Jean Auguste and Muris, Chris and Magnus, Jan R., Expected Utility and Catastrophic Risk in a Stochastic Economy-Climate Model (November 26, 2010). CentER Discussion Paper Series No. 2010-122. Available at SSRN: https://ssrn.com/abstract=1719053 or http://dx.doi.org/10.2139/ssrn.1719053

Masako Ikefuji

University of Tsukuba ( email )

Tsukuba University , Ibaraki Ken
Tsukuba, Ibaraki 305-8573, Ibaraki 3050006
Japan

Roger Jean Auguste Laeven (Contact Author)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Valckenierstraat 65-67
Amsterdam, 1018 XE
Netherlands
+31 20 525 4252 (Phone)

HOME PAGE: http://www.rogerlaeven.com

Chris Muris

affiliation not provided to SSRN ( email )

Jan R. Magnus

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081HV
Netherlands

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