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The interest rate for saving as a possibilistic risk

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  • Irina Georgescu
  • Jani Kinnunen

Abstract

In the paper there is studied an optimal saving model in which the interest-rate risk for saving is a fuzzy number. The total utility of consumption is defined by using a concept of possibilistic expected utility. A notion of possibilistic precautionary saving is introduced as a measure of the variation of optimal saving level when moving from a sure saving model to a possibilistic risk model. A first result establishes a necessary and sufficient condition that the presence of a possibilistic interest-rate risk generates an extra-saving. This result can be seen as a possibilistic version of a Rothschilld and Stiglitz theorem on a probabilistic model of saving. A second result of the paper studies the variation of the optimal saving level when moving from a probabilistic model (the interest-rate risk is a random variable) to a possibilistic model (the interest-rate risk is a fuzzy number).

Suggested Citation

  • Irina Georgescu & Jani Kinnunen, 2019. "The interest rate for saving as a possibilistic risk," Papers 1908.00445, arXiv.org.
  • Handle: RePEc:arx:papers:1908.00445
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    References listed on IDEAS

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    1. Donatella Baiardi & Marco Magnani & Mario Menegatti, 2014. "Precautionary saving under many risks," Journal of Economics, Springer, vol. 113(3), pages 211-228, November.
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    3. Gunning, Jan Willem, 2010. "Risk and savings: A taxonomy," Economics Letters, Elsevier, vol. 107(1), pages 39-41, April.
    4. Marco Magnani & Mario Menegatti, 2015. "Precautionary saving and changes in risk correlation," Economics Bulletin, AccessEcon, vol. 35(1), pages 561-570.
    5. Hayne E. Leland, 1968. "Saving and Uncertainty: The Precautionary Demand for Saving," The Quarterly Journal of Economics, Oxford University Press, vol. 82(3), pages 465-473.
    6. Dreze, Jacques H. & Modigliani, Franco, 1972. "Consumption decisions under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(3), pages 308-335, December.
    7. Marco Magnani, 2017. "A new interpretation of the condition for precautionary saving in the presence of an interest-rate risk," Journal of Economics, Springer, vol. 120(1), pages 79-87, January.
    8. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    9. L. Eeckhoudt & C. Gollier & H. Schlesinger, 2005. "Economic and financial decisions under risk," Post-Print hal-00325882, HAL.
    10. repec:fzy:fuzeco:v:21:y:2016:i:2:p:47-70 is not listed on IDEAS
    11. 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.
    12. Christophe Courbage & Béatrice Rey, 2007. "Precautionary saving in the presence of other risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 417-424, August.
    13. 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.
    14. A. Sandmo, 1970. "The Effect of Uncertainty on Saving Decisions," Review of Economic Studies, Oxford University Press, vol. 37(3), pages 353-360.
    15. Georgescu, Irina, 2008. "Possibilistic Risk Aversion," Working Papers 476, IAMSR, Åbo Akademi.
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