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Expected Utility and Catastrophic Risk

Author

Listed:
  • Masako Ikefuji

    (University of Southern Denmark, Denmark)

  • Roger Laeven

    (University of Amsterdam, the Netherlands)

  • Jan Magnus

    (VU University Amsterdam, the Netherlands)

  • Chris Muris

    (Simon Fraser University, Canada)

Abstract

An expected utility based cost-benefit analysis is in general fragile to its distributional assumptions. We derive necessary and sufficient conditions on the utility function of the expected utility model to avoid this. The conditions ensure that expected (marginal) utility remains finite also under heavy-tailed distributional assumptions. Our results are context-free and are relevant to many fields encountering catastrophic risk analysis, such as, perhaps most noticeably, insurance and risk management.

Suggested Citation

  • Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2014. "Expected Utility and Catastrophic Risk," Tinbergen Institute Discussion Papers 14-133/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140133
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    References listed on IDEAS

    as
    1. Chanel, Olivier & Chichilnisky, Graciela, 2013. "Valuing life: Experimental evidence using sensitivity to rare events," Ecological Economics, Elsevier, vol. 85(C), pages 198-205.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Jérôme Foncel & Nicolas Treich, 2005. "Fear of Ruin," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 289-300, December.
    4. Kenneth J. Arrow, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Response," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 136-138.
    5. Chichilnisky, Graciela, 2000. "An axiomatic approach to choice under uncertainty with catastrophic risks," Resource and Energy Economics, Elsevier, vol. 22(3), pages 221-231, July.
    6. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
    7. Christopher A. Sims, 2001. "Pitfalls of a Minimax Approach to Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 51-54, May.
    8. Robert S. Pindyck, 2011. "Fat Tails, Thin Tails, and Climate Change Policy," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 258-274, Summer.
    9. Geweke, John, 2001. "A note on some limitations of CRRA utility," Economics Letters, Elsevier, vol. 71(3), pages 341-345, June.
    10. Kenneth Arrow, 2009. "A note on uncertainty and discounting in models of economic growth," Journal of Risk and Uncertainty, Springer, vol. 38(2), pages 87-94, April.
    11. Denuit Michel & Dhaene Jan & Goovaerts Marc & Kaas Rob & Laeven Roger, 2006. "Risk measurement with equivalent utility principles," Statistics & Risk Modeling, De Gruyter, vol. 24(1), pages 1-25, July.
    12. Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
    13. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, November.
    14. Masako Ikefuji & Roger Laeven & Jan Magnus & Chris Muris, 2013. "Pareto utility," Theory and Decision, Springer, vol. 75(1), pages 43-57, July.
    15. Buchholz, Wolfgang & Schymura, Michael, 2012. "Expected utility theory and the tyranny of catastrophic risks," Ecological Economics, Elsevier, vol. 77(C), pages 234-239.
    16. Peter C. Fishburn, 1976. "Unbounded Utility Functions in Expected Utility Theory," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 163-168.
    17. Necir, Abdelhakim & Meraghni, Djamel, 2009. "Empirical estimation of the proportional hazard premium for heavy-tailed claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 49-58, August.
    18. William D. Nordhaus, 2011. "The Economics of Tail Events with an Application to Climate Change," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 5(2), pages 240-257, Summer.
    19. William D. Nordhaus, 2009. "An Analysis of the Dismal Theorem," Cowles Foundation Discussion Papers 1686, Cowles Foundation for Research in Economics, Yale University.
    20. Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A., 2010. "Decision principles derived from risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 294-302, December.
    21. Laeven, Roger J.A. & Goovaerts, Marc J. & Hoedemakers, Tom, 2005. "Some asymptotic results for sums of dependent random variables, with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 154-172, October.
    22. Peng, Liang, 2001. "Estimating the mean of a heavy tailed distribution," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 255-264, April.
    23. Terence M. Ryan, 1974. "The Use of Unbounded Utility Functions in Expected-Utility Maximization: Comment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 88(1), pages 133-135.
    24. -, 2009. "The economics of climate change," Sede Subregional de la CEPAL para el Caribe (Estudios e Investigaciones) 38679, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
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    Cited by:

    1. Ikefuji, M. & Laeven, R.J.A. & Magnus, J.R. & Muris, C.H.M., 2010. "Scrap Value Functions in Dynamic Decision Problems," Discussion Paper 2010-77, Tilburg University, Center for Economic Research.
    2. Chanel, Olivier & Chichilnisky, Graciela, 2013. "Valuing life: Experimental evidence using sensitivity to rare events," Ecological Economics, Elsevier, vol. 85(C), pages 198-205.
    3. Auke Hoekstra & Maarten Steinbuch & Geert Verbong, 2017. "Creating Agent-Based Energy Transition Management Models That Can Uncover Profitable Pathways to Climate Change Mitigation," Complexity, Hindawi, vol. 2017, pages 1-23, December.
    4. David Comerford, 2013. "A balance of questions: what can we ask of climate change economics?," Edinburgh School of Economics Discussion Paper Series 216, Edinburgh School of Economics, University of Edinburgh.

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    More about this item

    Keywords

    Expected utility; Catastrophe; Cost-benefit analysis; Risk management; Power utility; Exponential utility; Heavy tails;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics

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