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New results on high-order risk changes

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  • Menegatti, Mario

Abstract

This note extends the results on the first four derivatives of the utility function by Menegatti (Eur. J. Oper. Res. 232 (2014) 613–617) to the case of high-order derivatives. We show that, under usual assumptions, if the generic derivative of the utility function of order n is sign invariant then all the derivatives from order n to order 2 alternate in sign. We then focus on the case where the derivative of the utility function of order n is either positive when n is odd or negative when n is even, and we show the implications of this result for high-order risk changes and for saving decisions.

Suggested Citation

  • Menegatti, Mario, 2015. "New results on high-order risk changes," European Journal of Operational Research, Elsevier, vol. 243(2), pages 678-681.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:2:p:678-681
    DOI: 10.1016/j.ejor.2014.12.023
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    1. Eeckhoudt, Louis & Schlesinger, Harris & Tsetlin, Ilia, 2009. "Apportioning of risks via stochastic dominance," Journal of Economic Theory, Elsevier, vol. 144(3), pages 994-1003, May.
    2. Denuit, Michel M. & Eeckhoudt, Louis, 2010. "Stronger measures of higher-order risk attitudes," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2027-2036, September.
    3. Kimball, Miles S, 1993. "Standard Risk Aversion," Econometrica, Econometric Society, vol. 61(3), pages 589-611, May.
    4. Eeckhoudt, Louis & Schlesinger, Harris, 2008. "Changes in risk and the demand for saving," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1329-1336, October.
    5. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    6. W. Chiu & Louis Eeckhoudt, 2010. "The effects of stochastic wages and non-labor income on labor supply: update and extensions," Journal of Economics, Springer, vol. 100(1), pages 69-83, May.
    7. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    8. Courbage, Christophe & Rey, Béatrice, 2012. "Priority setting in health care and higher order degree change in risk," Journal of Health Economics, Elsevier, vol. 31(3), pages 484-489.
    9. Caballe, Jordi & Pomansky, Alexey, 1996. "Mixed Risk Aversion," Journal of Economic Theory, Elsevier, vol. 71(2), pages 485-513, November.
    10. Michel M. Denuit & Louis Eeckhoudt, 2013. "Risk attitudes and the value of risk transformations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 245-254, September.
    11. Donatella Baiardi & Mario Menegatti, 2011. "Pigouvian tax, abatement policies and uncertainty on the environment," Journal of Economics, Springer, vol. 103(3), pages 221-251, July.
    12. Patrick Roger, 2011. "Mixed risk aversion and preference for risk disaggregation: a story of moments," Theory and Decision, Springer, vol. 70(1), pages 27-44, January.
    13. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    14. Choi, Sungyong & Ruszczynski, Andrzej, 2011. "A multi-product risk-averse newsvendor with exponential utility function," European Journal of Operational Research, Elsevier, vol. 214(1), pages 78-84, October.
    15. Pratt, John W & Zeckhauser, Richard J, 1987. "Proper Risk Aversion," Econometrica, Econometric Society, vol. 55(1), pages 143-154, January.
    16. Menegatti, Mario, 2001. "On the Conditions for Precautionary Saving," Journal of Economic Theory, Elsevier, vol. 98(1), pages 189-193, May.
    17. Patrick L. Brockett & Linda L. Golden, 1987. "A Class of Utility Functions Containing all the Common Utility Functions," Management Science, INFORMS, vol. 33(8), pages 955-964, August.
    18. Finkelshtain, Israel & Kella, Offer & Scarsini, Marco, 1999. "On risk aversion with two risks," Journal of Mathematical Economics, Elsevier, vol. 31(2), pages 239-250, March.
    19. Christophe Courbage & Béatrice Rey, 2012. "Priority setting in health care and higher order degree change in risk," Post-Print halshs-03353458, HAL.
    20. Menegatti, Mario, 2014. "New results on the relationship among risk aversion, prudence and temperance," European Journal of Operational Research, Elsevier, vol. 232(3), pages 613-617.
    21. Denuit, Michel & Eeckhoudt, Louis, 2013. "Risk attitudes and the value of risk transformations," LIDAM Reprints ISBA 2013040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    22. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
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    Cited by:

    1. Crainich, David & Eeckhoudt, Louis & Menegatti, Mario, 2016. "Changing risks and optimal effort," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 97-106.
    2. Mensah, Edouard R. & Filipski, Mateusz J., 2022. "Saving for a rainy day: the impact of natural disasters on savings rates," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322266, Agricultural and Applied Economics Association.
    3. 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.
    4. Liudong Chen & Bolun Xu, 2024. "Prudent Price-Responsive Demands," Papers 2405.16356, arXiv.org.
    5. De Donno, Marzia & Menegatti, Mario, 2022. "On the relationship between comparisons of risk aversion of different orders," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    6. Marzia De Donno & Mario Menegatti, 2020. "Some conditions for the equivalence between risk aversion, prudence and temperance," Theory and Decision, Springer, vol. 89(1), pages 39-60, July.
    7. 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.
    8. Marzia Donno & Marco Magnani & Mario Menegatti, 2020. "Changes in multiplicative risks and optimal portfolio choice: new interpretations and results," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 251-267, June.
    9. Christophe Courbage & Henri Loubergé & Béatrice Rey, 2018. "On the properties of high-order non-monetary measures for risks," The Geneva Papers on Risk and Insurance Theory, Springer;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(1), pages 77-94, May.
    10. 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.
    11. 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.
    12. 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.
    13. Brianti, Marco & Magnani, Marco & Menegatti, Mario, 2018. "Optimal choice of prevention and cure under uncertainty on disease effect and cure effectiveness," Research in Economics, Elsevier, vol. 72(2), pages 327-342.

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