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Robust Comparative Statics of Risk Changes

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  • Diego C. Nocetti

    (School of Business, Clarkson University, Potsdam, New York 13699)

Abstract

The standard method for establishing the comparative statics of risk changes in optimization problems has been confined to comparing unique interior solutions, relying on strong assumptions about payoff functions and decision variables. We propose a simple and intuitive approach that hinges on considerably weaker assumptions. Merging insights from the monotone comparative statics literature with insights from the risk apportionment literature, we show that the ranking of simple lottery pairs is all that is needed for establishing the comparative statics of risk changes. We use this approach to analyze the comparative statics of N th-degree stochastic dominance shifts in a general setting with one and with multiple decision variables, and we show how these results can be applied to generalize the classical theories of precautionary saving, self-protection, and others. This paper was accepted by James Smith, decision analysis .

Suggested Citation

  • Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.
    • Handle: RePEc:inm:ormnsc:v:62:y:2016:i:5:p:1381-1392
    DOI: 10.1287/mnsc.2015.2202
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    Cited by:

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    4. Christoph Heinzel & Richard Peter, 2021. "Precautionary motives with multiple instruments [Motifs de précaution en cas de multiples instruments]," Working Papers hal-03484875, HAL.
    5. Gollier, Christian, 2021. "A general theory of risk apportionment," Journal of Economic Theory, Elsevier, vol. 192(C).
    6. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2020. "The theory of precautionary saving: an overview of recent developments," Review of Economics of the Household, Springer, vol. 18(2), pages 513-542, June.
    7. Mario Menegatti & Richard Peter, 2022. "Changes in Risky Benefits and in Risky Costs: A Question of the Right Order," Management Science, INFORMS, vol. 68(5), pages 3625-3634, May.
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    9. Antoine Bommier & François Le Grand, 2019. "Risk Aversion and Precautionary Savings in Dynamic Settings," Management Science, INFORMS, vol. 65(3), pages 1386-1397, March.
    10. Camacho, Carmen & Kamihigashi, Takashi & Sağlam, Çağrı, 2018. "Robust comparative statics for non-monotone shocks in large aggregative games," Journal of Economic Theory, Elsevier, vol. 174(C), pages 288-299.
    11. Mario Menegatti, 2018. "Prudence and Different Kinds of Prevention," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 44(2), pages 273-285, April.
    12. Paan Jindapon & Liqun Liu & William S. Neilson, 2021. "Comparative risk apportionment," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 91-112, April.
    13. Wang, Hongxia & Wang, Jianli & Li, Jingyuan & Xia, Xinping, 2015. "Precautionary paying for stochastic improvements under background risks," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 180-185.
    14. Wang, Jianli & Wang, Hongxia & Yick, Ho Yin, 2019. "How do changes in risk and risk aversion affect self-protection with Selden/Kreps–Porteus preferences?," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 1-6.
    15. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    16. Dennis W. Jansen & Liqun Liu, 2022. "Portfolio choice in the model of expected utility with a safety-first component," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 187-207, June.
    17. Heinzel, Christoph & Peter, Richard, 2021. "Precautionary motives with multiple instruments," Working Papers 316521, Institut National de la recherche Agronomique (INRA), Departement Sciences Sociales, Agriculture et Alimentation, Espace et Environnement (SAE2).
    18. Wong, Kit Pong, 2017. "A note on risky targets and effort," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 27-30.
    19. Rachel J. Huang & Larry Y. Tzeng & Lin Zhao, 2020. "Fractional Degree Stochastic Dominance," Management Science, INFORMS, vol. 66(10), pages 4630-4647, October.
    20. Liqun Liu & William S. Neilson, 2019. "Alternative Approaches to Comparative n th-Degree Risk Aversion," Management Science, INFORMS, vol. 65(8), pages 3824-3834, August.
    21. Ebert, Sebastian & van de Kuilen, Gijs, 2015. "Experiments on bivariate risk preferences," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113055, Verein für Socialpolitik / German Economic Association.
    22. Mario Menegatti, 2016. "A note on portfolio selection and stochastic dominance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 327-331, November.
    23. Heinzel, Christoph & Peter, Richard, 2023. "Precaution with multiple instruments: The importance of substitution effects," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 392-412.
    24. Bar Light, 2019. "Stochastic Comparative Statics in Markov Decision Processes," Papers 1904.05481, arXiv.org, revised Jan 2020.

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