Skip to main content

Robust management of climate risk damages


We consider the case of a risk manager or policymaker who does not know the true climate and economic parameters of the Dynamic Integrated Climate Economy (DICE) model and who, because of political or social constraints, cannot act optimally. We find that the impact of parameter uncertainty on economic outcomes is much more pronounced away from optimality than along an optimal path. We also find that for this non-omniscient and politically constrained actor the most desirable of the feasible courses of actions depends strongly on which model is most uncertain. When we consider uncertainty in the growth rate of the economy or in the cost of abatement, a gradual ramp-up is preferred to a steep (‘Stern-like’) abatement schedule. This result is extremely robust to the choice of a number of non-expected-utility-maximization decisional criteria that do not make use of probabilities: minimax, maximax and maximin all give the same recommendation. Ambiguity aversion does not change these results. However, when even a small uncertainty in the damage function is considered, a steeper abatement schedule becomes a strong contender, and is preferred by some decisional criteria. Furthermore, the ‘cross-over point’ for the damage exponent (the point, that is, above which an aggressive abatement schedule becomes preferred) is very close to the DICE value. This suggests that researching this aspect of climate modelling would have the greatest policy relevance. Finally, we note that a gradual (‘Nordhaus-like’) ramp-up of the abatement efforts abatement schedule is always preferred to a slower (‘business-as-usual’) schedule of abatement even in the case of much stronger future economic growth or much milder climate damage than the central estimates of the DICE model.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9


  1. IPCC Report (2014), Chapter 4, Strengthening and Implementing the Global Response, Sect., p. 321.

  2. A description of earlier versions of the model, and the changes to the model and its parameters, can be found in Nordhaus and Sztorc (2013). The structure of the model and its relationship to similar IAMs can be found in Nordhaus and Moffat (2017) and Nordhaus (2007b). The links between the DICE model and DSGE models are discussed in detail in Hassler et al. (2016).

  3. Dietz et al. (2007) claim that a non-aggressive ramp-up can only by justified by those who deny the anthropogenic origin of climate change; by those who stress the adaptability of the human species; and by ‘those who accept the science of climate change and the likelihood that it will inflict heavy costs, but simply do not care much for what happens in the future beyond the next few decades’. Several other authors take objection to this characterization: see, e.g. Dasgupta (2008, 2020); Nordhaus and Moffat (2017); Nordhaus (2007c).

  4. It is extremely difficult if not impossible to meaningfully estimate discount rates for future costs and benefits [...] Thus standard cost–benefit analyses become difficult to justify [...] and are not used as an assessment tool in this report’. IPPC (2014), Chapter 1, p. 76.

  5. Constrained policies are also considered in Nordhaus (2007b); however, these still explore the optimal policies consistent with the achievement of exogenous targets, such as a maximum acceptable increase in the temperature anomaly by a certain date. As discussed in Sect. 2, Tol (2020) also considers policy actions away from optimality, but from the perspective of a ‘selfish bureaucrat’ is the spirit of Niskanen (1960).

  6. ‘A possible explanation of the carbon pricing puzzle is based on the existence of political constraints related to the social acceptability of climate policies...’, Gollier (2020), p. 5, emphasis added.

  7. Parameter uncertainty in IAM models is usually dealt with by calculating the optimal paths associated with parameter sets drawn from a posited parameter distribution. Needless to say, this falls well short of reaching a decision on the basis of a procedure that feeds the uncertainty into a convex utility function.

  8. Here we use the term ‘risk’ to denote collectively what Knight (1957/2006) describes as ‘a priori probability’ and ‘statistical probability’, and we use the term ‘uncertainty’ to denote what he call ‘estimates’. See p. 225.

  9. The precise definition of the Gradual, Aggressive and Slow schedules is given in Sect. 5.

  10. The decarbonization rate and the abatement costs are in the DICE model a deterministic function of time. We endogenize them in Sect. 5, but they become a function of cumulative investment efforts, not of economic growth.

  11. See Chapter 1 in particular.

  12. See p. 158 and passim.

  13. The value of the ‘utility impatience’ parameter of \(\beta\) of 0.0010 chosen by Stern does not even allow for a very modest reduction of the degree of concern for the welfare of infinitely distant generations: it is only meant to cater for the probability that humanity may be wiped out by an asteroid-like event. If this stance is taken, arguably the possibility of a nuclear war or of a global pandemic—which currently appear vastly more likely than the impact of an asteroid—should raise the discount rate above 0.0010.

  14. We follow and further the cost–benefit analyses of climate change in the line of Nordhaus (2008), Stern (2007), and Hope (2006, 2013) and related IAMs. We are aware of objections such as those in Pindyck (2013), who have criticized these cost–benefit analyses for their unrealistic assumptions, but we consider the addressing of these concerns beyond the scope of this work.

  15. A vibrant strand of current research tries to link the DICE model with non-separable utility functions. These invariably make use of some variant of the Bellman equation. See, e.g. Cai et al. (2015b), Ackerman et al. (2013), Daniel et al. (2018). Due to the computational challenges, a full application of the DICE model to a recursive-utility setting is still very incomplete, but it appears that static risk aversion plays a much smaller role than aversion to intergenerational inequality of consumption, which the elasticity of marginal utility chosen in the DICE model (1.45) tries to capture.

  16. Tol (2020) also considers the effect of policy heterogeneity.

  17. Joughin et al. (2014) argue that marine west Antarctic ice sheet collapse is already under way, while Lenton et al. (2008) evaluate that the Greenland ice sheet melting could lead to a global sea level rise of up to one metre per century. The risk of multiple interacting tipping points is also discussed by Cai et al. (2016).

  18. In this paper, we do not consider the effect of uncertainty in the utility discount rate—if of ‘uncertainty’ one can speak in this case—but we do consider uncertainty in the growth rate of the economy, which is one component of the Ramsey-equation discount rate. For a general and in-depth discussion of uncertainty in climate modelling see Brock and Hansen (2018). For a discussion of the effect of uncertainty in the discount rate, see Weitzman (1998). The attending debate about gamma discounting with Gollier can be found in Gollier (2002, 2004), and the resolution of its ‘paradox’ in Gollier (2010).

  19. The paper by Woodward and Bishop (1997) was based on one of the first versions of the DICE model. The model output have changed both because of different parameter choices and improved modelling.

  20. The output available for non-abatement investment and consumption, y is given by \(y= y_{gross}\left( 1-damfrac-abatefrac\right)\), with abatefrac equal to the fraction of output devoted to abatement efforts. See Sect. 4 for a detailed discussion.

  21. To facilitate cross-referencing with the DICE model, we have used the same symbols for the variables used in this paper as the variable names in the GAMS code of the DICE model made public by Prof Nordhaus.

  22. Apart from the need to break the non-sensical link between high carbon intensity and high negative emissions for values of \(\mu\) above 1, Barreto and Kypreos (1999) confirm that endogenizing technological progress produces significantly different outcomes when it comes to modelling energy systems.

  23. 2014 is the closest date to the release date of the version of the DICE model (2016) that we use.

  24. We say ‘implicit’ because a social discount rate is obtained by the first-order Euler condition at the optimum: for ‘small’ (marginal) investments. The DICE approach obtains, and does not start from, optimality, and does not require the investment to be ‘small’.

  25. In different contexts, the utility discount factor is often referred to as the ‘impatience’ parameter. This interpretation is unwarranted when intergenerational utilities are aggregated. Therefore we do not use the term impatience.

  26. Available at

  27. This limit is discussed in Sect. 4.

  28. The far right tail of the Slow abatement schedule is numerically unreliable: given the high discount rate, the discount factor for horizons over two centuries becomes extremely small (the utility discount factor for the final horizon of 500 year is \(2.5 ^{-8}\)), and therefore large changes in distant consumptions have a negligible effect on the target function. Indeed, for the Slow optimal schedule the default optimization routines offered by two popular software packages—the MatLab function fminunc which uses the quasi-Newton algorithm, and the Python function minimize of the Jones et al. (2001) package SciPy which uses the SLSQP method—generate significantly different behaviours for the abatement fraction at the very long end, but produce a virtually identical total utilities.

  29. ‘Forcing’ is the balance of energy in and energy out for the Earth system, i.e. the difference between solar irradiance absorbed by the Earth, and the energy radiated (not reflected) back into space via black-body radiation. Reflection is accounted for, via albedo, as an effective reduced irradiance.

  30. The concentrations for the RCPs are CO2 equivalent gases, aggregating gases under the Kyoto Protocols. The CO2 concentration fo the DICE model is what is referred to in the documentation as ‘concentration in the upper strata’.

  31. The technical meaning of the term ‘likely’ in the IPCC reports is ‘with likelihood higher than 66%’.

  32. This is true by construction for the ‘objective’ schedules, but happens to be approximately true as well for the subjective schedules—confirming again that the subjective schedules have been reasonably chosen.

  33. The values for \(K_1\) and \(K_2\) are 0.03025 and \(-10,993.704\), respectively.

  34. Several other non-probabilistic criteria have been proposed, such as the \(\alpha\)-maximin criterion, defined by \(\max _{a \in A} [\alpha \min _{s \in S} a(s) + (1-\alpha ) \max _{s \in S} a(s)]\) by Arrow and Hurwicz (2010). However, they often depend on an arbitrary ‘mixing’ parameter \(\alpha\). A detailed analysis over a range of possible values for \(\alpha\) would make the present work, already very rich in permutations, too heavy.

  35. Actually, we simply impose the milder requirement that the social planner only knows the first two moments of the distribution of the parameter values. Given this level of knowledge, a Guassian distribution is the corresponding maximum-entropy distribution. The planner therefore uses the discrete probabilities \(q_i\) associated with a Gaussian density with these two moments. For the optimization over five values the discrete probabilities were chosen to be \(q_{\pm 40\%}=0.13\), \(q_{\pm 25\%}=0.20\) and \(q_{0}=0.34\).

  36. For ease of cross-reference with the DICE code we use in this section the symbols and variable names used in the DICE code.

  37. “...An important example that has been used in policy discussions is an approach which assumes a sharp threshold at a temperature increase of 2 C; implicitly this implies a very sharp kink in the curve near that threshold...’, p. 16.

  38. “...By far the most important uncertain variable for climatic outcomes is the growth in total factor productivity. This is the main driver of economic growth in the long run, and output trends tend to dominate emissions and therefore climate change...” Nordhaus (2007b), p. 109.

  39. emphasis added.

  40. This value refers to an earlier version of the DICE model, and the expected growth per annum cannot therefore be directly compared. The standard deviation, however, should be more transportable. See the discussion on p. 226 of Nordhaus (2007b).

  41. We note again that there are no reasonable values of the damage exponent for a cross-over between the Gradual and Slow schedules to occur. We also note that, for damage exponents below thresholds in the range of values between 1.75 and 2.45 the Slow schedules can have a greater discounted utility than the Aggressive schedules.

  42. A case has been made [see, e.g. Lovejoy (2019)] that not only the weather, but also the climate may be governed by chaotic-dynamics behaviour, with fat-tailed (power-law) outcomes. This would clearly require far deeper changes of the DICE equations than altering its parameters, and is beyond the scope of our study.

  43. See, in particular, Chapter 20, Must a concern for the environment be centred on human beings?.


  • Ackerman, F., E.A. Stanton, and R. Bueno. 2013. Epstein-Zin Utility in DICE: Is Risk Aversion Irrelevant to Climate Policy? Environmental and Resource Economics 56 (1): 73–84.

    Article  Google Scholar 

  • Altug, S., C. Cakmakli, F. Collard, S. Mukerji, and H. Ozsoylev. 2010. Ambiguous Business Cycles: A Quantitative Assessment. Review of Economic Dynamics 38 (October): 220–237.

    Google Scholar 

  • Anthoff, D., and R.S.J. Toll. 2016. Shutting Down the Thermohaline Circulation. American Economic Review 106 (5): 602–06.

    Article  Google Scholar 

  • Arrow, K., and L. Hurwicz. 2010. An Optimality Criterion for Decision-Making Under Ignorance. In Studies in Resource Allocation Processes, 482. Cambridge: Cambridge University Press.

  • Barnett, M., W. Brock, and L.P. Hansen. 2020. Pricing Uncertainty Induced by Climate Change. The Review of Financial Studies 33 (3): 1024–1066.

    Article  Google Scholar 

  • Barreto, L., and S. Kypreos. 1999. Technological Learning in Energy Models: Experience and Scenario Analysis with MARKAL and the ERIS Model Prototype. Paul Scherrer Institute Technical Report PSI Bericht 99-08, 1–34, Switzerland.

  • Bellman, R. 1957. Dynamic Programming. Princeton: Princeton University Press, OCLC: 526246.

  • Bellman, R., and S.E. Dreyfus. 1962. Applied Dynamic Programming. Princeton: Princeton University Press.

    Book  Google Scholar 

  • Bems, R., and L. Juvenal. 2022. Climate Change Mitigation Will Cause Large Adjustments in Current Account Balances. IMF Report, 1–5, August 16, 2022.

  • Biskaborn, B.K., S. Smith, and J. Noetzli. 2010. Permafrost is Warming at a Global Scale. Nature Communications.

    Article  Google Scholar 

  • Bosetti, V., C. Carraro, M. Galeotti, E. Massetti, and M. Tamoni. 2006. World Induced Technical Change Hybrid Model. Energy Journal Special Issue no 2: 13–38.

    Google Scholar 

  • Brock, W., and L.P. Hansen. 2018. Wrestling with Uncertainty in Climate Economic Models. University of Chicago, Working Paper, Macro Finance Research Program, 1–71.

  • Cai, Y., K. Judd, T.M. Lenton, T. Lontzek, and D. Narita. 2015a. Environmental Tipping Points Significantly Affect the Cost-Benefit Assessment of Climate Policies. Proceedings of the National Academy of Sciences of the United States of America 112 (15): 4606–4611.

    Article  Google Scholar 

  • Cai, Y., K. Judd, and T. Lontzek. 2015b. The Social Cost of Carbon with Economic and Climate Risks. Journal of Political Economy 127: 2684–2734.

    Article  Google Scholar 

  • Cai, Y., T.M. Lenton, and T.S. Lontzek. 2016. Risk of Multiple Interacting Tipping Points Should Encourage Rapid CO2 Emission Reduction. Nature Climate Change 6 (5): 520–525.

    Article  Google Scholar 

  • Chakravorty, U., M. Moreaux, and M. Tidball. 2008. Ordering the Extraction of Polluting Non Renewable Resources. American Economic Review 98: 1128–1144.

    Article  Google Scholar 

  • Christensen, P., K. Gillingham, and W. Nordhaus. 2018. Uncertainty in Forecasts of Long-Run Economic Growth. In PNAS, ed. W.C. Clark. Cambridge.

  • Clarke, L., J. Edmonds, H. Jacoby, Pitcher, Reilly, and Richels. 2009. Scenarios of Greenhouse Gas Emissions and Atmospheric Concentrations. Sub-report 2.1—A of Synthesis and Assessment Product 2.1 by the U.S. Climate Change Science Program and the Subcommittee on Global Change Research, vol. 112, no. 3, 373–391. Washington DC: Department of Energy, Office of Biological and Environmental Research.

  • Clarke, L.E., and J. Weyant. 2002. Modeling Induced Technical Change: An Overview. In Technological Change and the Environment. Resources for the Future, ed. A. Grubler, N. Nakicenovic, and W.D. Nordhaus. Washington, D.C.

  • Cline, W. 1992. The Economics of Global Warming. Washington, D.C.: Institute for International Economics.

    Google Scholar 

  • Daniel, K.D., and R.B. Litterman, and G. Wagner. 2018. Applying Asset Pricing Theory to Calibrate the Price of Climate Risk. Working Paper 22795, 1–51. National Bureau of Economic Research.

  • Dasgupta, P. 2008. Discounting Climate Change. Journal of Risk and Uncertainty 37: 141–169.

    Article  Google Scholar 

  • Dasgupta, P. 2020. Ramsey and Intergenerational Welfare Economics. In The Stanford Encyclopedia of Philosophy, ed. E.N. Zalta, summer 2020 ed. Metaphysics Research Lab, Stanford University.

  • de Bruin, K., and C.K. Krishnamurthy. 2021. Optimal Climate Policy with Fat-Tailed Uncertainty—What the Models Can Tell Us. ESRI Working Paper, Working Paper No. 697(March 2021), 1–23.

  • Dietz, S., C. Hope, N. Stern, and D. Zenghelis. 2007. Reflections on the Stern Review: A Robust Case for Strong Action to Reduce the Risks of Climate Change. World Economics 8 (1): 121–168.

    Google Scholar 

  • Drupp, M.A., M.C. Freeman, B. Groom, and F. Nesje. 2015. Discounting Disentangled: An Expert Survey on the Determinants of the Long-Term Social Discount Rate. Working Paper, 1/54. London School of Economics.

  • Dumas, L. 2023. Financial Stability, Stranded Assets and the Low-Carbon Transition—A Critical Review of the Theoretical and Applied Literatures. In Journal of Economic Surveys, Working Paper No. 697, 1–116.

  • Fujino, J., R. Nair, M. Kainuma, T. Masui, and Y. Matsuoka. 2006. Multi-gas Mitigation Analysis on Stabilization Scenarios Using AIM Global Model. Multigas Mitigation and Climate Policy. The Energy Journal Special Issue 27: 343–353.

  • Gallant, A.R., M.R. Jahan-Prevar, and H. Liu. 2015. Measuring Ambiguity Aversion. Working Paper, Finance and Economics Discussion Series, 1/46.

  • Gollier, C. 2002. Discounting an Uncertain Future. Journal of Public Economics 85 (2): 149–166.

    Article  Google Scholar 

  • Gollier, C. 2004. Maximizing the Expected Net Future Value as an Alternative Strategy to Gamma Discounting. Finance Research Letters 1 (2): 85–89.

    Article  Google Scholar 

  • Gollier, C. 2010. How Should the Distant Future Be Discounted When Discount Rates Are Uncertain? Economics Letters 107: 350–353.

    Article  Google Scholar 

  • Gollier, C. 2013. Pricing the Planet’s Future: The Economics of Discounting in an Uncertain World. Oxford, Princeton: Princeton University Press.

    Google Scholar 

  • Gollier, C. 2020. The Cost-Efficiency Carbon Pricing Puzzle. Toulouse School of Economics Working Paper 18-952(February): 1–32.

  • Grauwe, P.D. 2019. The Limits of the Market. Oxford: Oxford University Press.

    Google Scholar 

  • Gruebler, A. 2004. Transitions in Energy Use, 1–16. Laxenburg: International Institute for Applied System Analysis.

  • Gruebler, A., and S. Messner. 1998. Technological Change and the Timing of Abatement Measures. Energy Economics 20: 495–512.

    Article  Google Scholar 

  • Gruebler, A., and N. Nakicenovic. 1996. Decarbonizing the Global Energy System. Technological Forecasting and Social Change 53: 97–110.

    Article  Google Scholar 

  • Gordon R.J. 2016. The Rise and Fall of American Growth Princeton University Press, Princeton, NJ

  • Hambel, C., H. Kraft, and E. Schwartz. 2021. Optimal Carbon Abatement in a Stochastic Equilibrium Model with Climate Change. European Economic Review 132: 103642.

    Article  Google Scholar 

  • Hassler, J., P. Krusell, and A. Smith. 2016. Chapter 24—Environmental Macroeconomics. In Handbook of Macroeconomics, vol. 2, 1893–2008. Elsevier.

  • Heal, G., and A. Millner. 2013. Uncertainty and Decision in Climate Change Economics. London School of Economics, Centre for Climate Change Economcis and Policy, Working Paper(108), 1–26.

  • Hijioka, Y., Y. Matsuoka, H. Nishimoto, M. Masui, and M. Kainuma. 2006. Global GHG Emissions Scenarios Under GHG Concentration Stabilization Targets. Journal of Global Environmental Engineering 13: 97–108.

    Google Scholar 

  • Hope, C. 2006. The Marginal Impact of CO2 from PAGE2002: An integrated Assessment Model Incorporating the IPCC’s Five Reasons for Concern. Integrated Assessment 6 (1): 1–26.

    Google Scholar 

  • Hope, C. 2013. Critical Issues for the Calculation of the Social Cost of CO2: Why the Estimates from PAGE09 Are Higher than Those from PAGE2002. Climatic Change 117 (3): 531–543.

    Article  Google Scholar 

  • Hotelling, H. 1931. The Economics of Exhaustible Resources. Journal of Political Economy 39 (2): 137–175.

    Article  Google Scholar 

  • IPCC. 2014. AR5 Climate Change 2014: Mitigation of Climate Change, Fifth Assessment report.

  • Jahan-Parvar, M.R., and H. Liu. 2014. Ambiguity Aversion and Asset Prices in Production Economies. Review of Financial Studies 27 (10): 3060–3097.

    Article  Google Scholar 

  • Jensen, S., and C.P. Traeger. 2014. Optimal Climate Change Mitigation Under Long-Term Growth Uncertainty: Stochastic Integrated Assessment and Analytic Findings. European Economic Review 69: 104–125.

    Article  Google Scholar 

  • Jones, E., T. Oliphant, P. Peterson, et al. 2001. SciPy: Open Source Scientific Tools for Python.

  • Joughin, I., B.E. Smith, and B. Medley. 2014. Marine Ice Sheet Collapse Potentially Under Way for the Thwaites Glacier Basin, West Antarctica. Science 344 (6185): 735–738.

    Article  Google Scholar 

  • Ju, N., and J. Miao. 2012. Ambiguity, learning, and asset returns. Econometrica 80 (2): 559–591.

  • Kim Y.E. and N.V. Loyaza 2019. Productivity Growth Patterns and Determinants across the World, World Bank working paper 8852.

  • Klibanoff, P., M. Marianacci, and S. Mukerji. 2005. A Smooth Model of Decision Making Under Ambiguity. Econometrica 73 (6): 1849–1892.

    Article  Google Scholar 

  • Knight, F.H. 1957/2006. Risk Uncertainty and Profit. Dover Publications, NY, NY

  • Lemoine, D., and C. Traeger. 2014. Watch Your Step: Optimal Policy in a Tipping Climate. American Economic Journal: Economic Policy 6 (1): 137–166.

    Google Scholar 

  • Lemoine, D., and C.P. Traeger. 2016. Ambiguous Tipping Points. Journal of Economic Behavior and Organization 132: 5–18.

    Article  Google Scholar 

  • Lenton, T.M., H. Held, E. Kriegler, J.W. Hall, W. Lucht, S. Rahmstorf, and H.J. Schellnhuber. 2008. Tipping Elements in the Earth’s Climate System. Proceedings of the National Academy of Sciences 105 (6): 1786–1793.

    Article  Google Scholar 

  • Lovejoy, S. 2019. Weather, Macroweather and the Climate. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Messner, S. 2013. Endogenized Technological Learning in an Energy System Model. Journal of Evolutionary Economics 7: 291–313.

    Article  Google Scholar 

  • Millner, A., S. Dietz, and G. Heal. 2013. Scientific Ambiguity and Climate Policy. Environmental and Resource Economics 55 (1): 21–46.

    Article  Google Scholar 

  • Niskanen, W.A. 1960. The Peculiar Economics of Bureaucracy. The American Economic Review 58 (2): 293–305.

    Google Scholar 

  • Nordhaus, W.D. 2007a. Accompanying Notes and Documentation on Development of DICE-2007 Model: Notes on as of July 25, 2007. New Haven: Yale University.

  • Nordhaus, W.D. 2007b. The Challenge of Global Warming: Economic Models and Environmental Policy. New Haven: Yale University.

    Google Scholar 

  • Nordhaus, W.D. 2007c. A Review of the Stern Review on the Economics of Climate Change. Journal of Economic Literature 45 (3): 687–702.

    Article  Google Scholar 

  • Nordhaus, W.D. 2008. An Analysis of the Dismal Theorem. Yale University Working Paper, New Haven.

  • Nordhaus, W.D. 2016. Projections and Uncertainties About Climate Change in an Era of Minimal Climate Policies. Discussion Paper w22933. National Bureau of Economic Research.

  • Nordhaus, W.D. 2017. Revisiting the Social Cost of Carbon. Proceedings of the National Academy of Sciences of the United States of America 114 (7): 1518–1523.

    Article  Google Scholar 

  • Nordhaus, W., and A. Moffat. 2017. A Survey of Global Impacts of Climate Change: Replication, Survey Methods, and a Statistical Analysis. NBER Working Papers 23646. National Bureau of Economic Research, Inc.

  • Nordhaus, W.D., and P. Sztorc. 2013. DICE 2013R: Introduction and User’s Manual. New Haven: Yale University.

    Google Scholar 

  • Olson, R., R. Sriver, M. Goes, N.M. Urban, H.D. Matthews, M. Haran, and K. Keller. 2012. A Climate Sensitivity Estimate Using Bayesian Fusion of Instrumental Observations and an Earth System Model. Journal of Geophysical Research: Atmospheres.

    Article  Google Scholar 

  • Pachauri, R.K., and L.A. Meyer. 2014. Climate Change 2014: Synthesis Report. Contribution of Working Groups I, II and III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Journal of Political Economy 39: 1–151.

    Google Scholar 

  • Picketty, T. 2014. Capital in the Twenty-First Century. Cambdridge: The Bellknap Press of Harvard University Press.

    Book  Google Scholar 

  • Pierrehumbert, R.T. 2010. Principles of Planetary Climate. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Pindyck, R.S. 2013. Climate Change Policy: What Do the Models Tell Us? Journal of Economic Literature 51 (3): 860–872.

    Article  Google Scholar 

  • Pindyck, R.E. 2022. Climate Future—Averting and Adapting to Climate Change. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Pontryagin, L.S., V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko. 1962. The Mathematical Theory of Optimal Processes. Geneva: Interscience Publishers.

    Google Scholar 

  • Ramsey, F.P. 1928. A Mathematical Theory of Saving. Economic Journal 45 (3): 543–559.

    Article  Google Scholar 

  • Rawls, J. 1972. A Theory of Justice. Oxford: Oxford University Press.

    Google Scholar 

  • Riahi, K., A. Gruebler, and N. Nakicenovic. 2007. Scenarios of Long-Term Socio-economic and Environmental Development Under Climate Stabilization. Technological Forecasting and Social Change 74 (7): 887–935.

    Article  Google Scholar 

  • Savage, L.J. 1954. The Foundations of Statistics. Chichester: Wiley.

    Google Scholar 

  • Seshadri, A.K. 2016. Decarbonization Rate and the Timing and Magnitude of the CO2 Concentration Peak. Global and Planetary Change 146 (November): 22–29.

    Article  Google Scholar 

  • Smith, S.J., and T.M.L. Wigley. 2006. Multi-gas Forcing Stabilization with the MiniCAM. The Journal of Energy 27, Special Issue (3): 373–391.

    Google Scholar 

  • Stern, N. 2007. The Economics of Climate Change: The Stern Review. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Tol, R.S.J. 2020. Selfish Bureaucrats and Policy Heterogeneity in Nordhaus’ DICE. Climate Change Economics 11 (4): 2040006.

    Article  Google Scholar 

  • van der Zwaan, B.C.C., R. Gerlach, G. Klassen, and L. Schrattenholzer. 2002. Endogenous Technological Change in Climate Change Modelling. Energy Economics 24: 1–19.

    Article  Google Scholar 

  • van Vuuren, D.P., M. den Elzen, P. Lucas, B. Eickhout, B. Strengers, B. van Ruijven, S. Wonink, and R. van Houdt. 2007. Stabilizing Greenhouse Gas Concentrations at Low Levels: An Assessment of Reduction Strategies and Costs. Climatic Change.

    Article  Google Scholar 

  • van Vuuren, D.P., E. Kriegler, B.C.O. Neil, K.L. Rihai, T. Carter, J. Edmonds, S. Allegatte, T. Kram, R. Mathur, and H. Winkler. 2011. A New Scenario Framework for Climate Change Research: Scenario Matrix Architecture. Climatic Change 122: 373–386.

    Article  Google Scholar 

  • Wald, A. 1949. Statistical Decision Functions. The Annals of Mathematical Statistics 20 (2): 165–205.

    Article  Google Scholar 

  • Weitzman, M.L. 1998. Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate. Journal of Environmental Economics and Management 36: 201–208.

    Article  Google Scholar 

  • Weitzman, M.L. 2009. On Modeling and Interpreting the Economics of Catastrophic Climate Change. The Review of Economics and Statistics 91 (1): 1–19.

    Article  Google Scholar 

  • Williams, B. 1995. Making Sense of Humanity and Other Philosophical Papers. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Wise, M.A., K. Calvin, A. Thomson, L. Clarke, B. Bond-Lamberty, R. Sands, S. Smith, A. Janetos, and J. Edmonds. 2009. Implications of Limiting CO2 Concentrations for Land Use and Energy. Science 324: 1183–1186.

    Article  Google Scholar 

  • Woodward, R.T., and R.C. Bishop. 1997. How to Decide When Experts Disagree: Uncertainty-Based Choice Rules in Environmental Policy. Land Economics 73 (4): 492–507.

    Article  Google Scholar 

  • Yumashev, D. 2020. PAGE-ICE Integrated Assessment Models. Working Paper, 1–29. Lancaster University(x).

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Riccardo Rebonato.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rebonato, R., Ronzani, R. & Melin, L. Robust management of climate risk damages. Risk Manag 25, 15 (2023).

Download citation

  • Accepted:

  • Published:

  • DOI:


JEL Classification