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Precautionary paying for stochastic improvements under background risks

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  • Wang, Hongxia
  • Wang, Jianli
  • Li, Jingyuan
  • Xia, Xinping

Abstract

In a two-dimensional framework, we propose a general two-period decision model which extends the temporal precautionary saving and effort model. We relate the role of cross-prudence to the impact of background risks on paying for stochastic improvements of the future risk. We find that the effect of background risks introduced in the first period is consistent to signing cross derivatives of bivariate utility functions, which is independent of the type of stochastic improvements brought by additional paying; however, when the background risk occurs in the second period, that is not the case.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:64:y:2015:i:c:p:180-185
    DOI: 10.1016/j.insmatheco.2015.05.012
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    as
    1. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2014. "Precautionary saving under many risks," Journal of Economics, Springer, vol. 113(3), pages 211-228, November.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. Courbage, Christophe & Rey, Béatrice, 2012. "Optimal prevention and other risks in a two-period model," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 213-217.
    4. Menegatti, Mario, 2009. "Optimal prevention and prudence in a two-period model," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 393-397, November.
    5. 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.
    6. Louis Eeckhoudt & Béatrice Rey & Harris Schlesinger, 2007. "A Good Sign for Multivariate Risk Taking," Management Science, INFORMS, vol. 53(1), pages 117-124, January.
    7. Louis Eeckhoudt & Rachel J. Huang & Larry Y. Tzeng, 2012. "Precautionary Effort: A New Look," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(2), pages 585-590, June.
    8. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    9. Cary Deck & Harris Schlesinger, 2014. "Consistency of Higher Order Risk Preferences," Econometrica, Econometric Society, vol. 82, pages 1913-1943, September.
    10. Louis Eeckhoudt & Harris Schlesinger, 2006. "Putting Risk in Its Proper Place," American Economic Review, American Economic Association, vol. 96(1), pages 280-289, March.
    11. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    12. David Crainich & Louis Eeckhoudt & Alain Trannoy, 2013. "Even (Mixed) Risk Lovers Are Prudent," American Economic Review, American Economic Association, vol. 103(4), pages 1529-1535, June.
    13. Diego C. Nocetti, 2016. "Robust Comparative Statics of Risk Changes," Management Science, INFORMS, vol. 62(5), pages 1381-1392, May.
    14. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, October.
    15. Ehrlich, Isaac & Becker, Gary S, 1972. "Market Insurance, Self-Insurance, and Self-Protection," Journal of Political Economy, University of Chicago Press, vol. 80(4), pages 623-648, July-Aug..
    16. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    17. Chiu, W.Henry, 2005. "Degree of downside risk aversion and self-protection," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 93-101, February.
    18. W Henry Chiu, 2012. "Risk Aversion, Downside Risk Aversion and Paying for Stochastic Improvements," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 37(1), pages 1-26, March.
    19. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, October.
    20. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    21. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    22. Sebastian Ebert, 2013. "Even (Mixed) Risk Lovers Are Prudent: Comment," American Economic Review, American Economic Association, vol. 103(4), pages 1536-1537, June.
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    Cited by:

    1. Peter, Richard, 2017. "Optimal self-protection in two periods: On the role of endogenous saving," Journal of Economic Behavior & Organization, Elsevier, vol. 137(C), pages 19-36.
    2. Heinzel Christoph & Richard Peter, 2021. "Precautionary motives with multiple instruments," Working Papers SMART 21-09, INRAE UMR SMART.
    3. 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.
    4. Crainich, David & Menegatti, Mario, 2021. "Self-protection with random costs," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 63-67.
    5. Mario Menegatti, 2018. "Prudence and Different Kinds of Prevention," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 44(2), pages 273-285, April.
    6. 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.
    7. Crainich, David & Eeckhoudt, Louis & Menegatti, Mario, 2016. "Changing risks and optimal effort," Journal of Economic Behavior & Organization, Elsevier, vol. 125(C), pages 97-106.
    8. Christoph Heinzel & Richard Peter, 2021. "Precautionary motives with multiple instruments [Motifs de précaution en cas de multiples instruments]," Working Papers hal-03484875, HAL.
    9. 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.
    10. 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).
    11. Desu Liu & Mario Menegatti, 2019. "Optimal saving and health prevention," Journal of Economics, Springer, vol. 128(2), pages 177-191, October.
    12. Wang, Hongxia & Wang, Jianli & Yin, Yick Ho, 2018. "Willingness to pay for stochastic improvements of future risk under different risk aversion," Economics Letters, Elsevier, vol. 168(C), pages 52-55.
    13. Liqun Liu & Andrew J. Rettenmaier & Thomas R. Saving, 2019. "Staying the Course or Rolling the Dice: Time Horizon’s Effect on the Propensity to Take Risk," Journal of Insurance Issues, Western Risk and Insurance Association, vol. 42(1), pages 66-85.

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    More about this item

    Keywords

    Background risk; Stochastic improvements; Cross-prudence; Precautionary saving; Precautionary effort;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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