Expected utility and catastrophic risk in a stochastic economy–climate model

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 economyclimate 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.

The missing risks of climate change

“…Economic assessments of scenarios, however, do not require optimization, and higher-resolution economic risk assessments have been produced for the United States and Europe 33 , the consequences of tipping points 50 and country-level-scale information using empirical damage estimates 51 . Improvements in stochastic optimization techniques also provide a pathway to increasing resolution while studying optimal mitigation 52 .…”

Synergy of climate change with country success and city quality of life

“…Optimization is not, however, required in economic assessments of scenarios 1 . Resolution while studying optimal mitigation can also be increased by making improvements in stochastic optimization techniques 37 . We used the RECASTM method in this study.…”

Growth and Mitigation Policies with Uncertain Climate Damage

“…Some of the integrated assessment models of climate change have recently also included dierent forms of uncertainty in their numerical simulation approaches, see, e.g., Pizer (1999), Ikefuji et al (2010), Jensen and Traeger (2011), Lontzek and Narita (2011), Cai et al (2013), and Lemoine and Traeger (2013). Contrary to these papers, we provide closed form model solution showing the exact impact of all the parameters.…”