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Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

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Listed:
  • Nicole El Karoui

    (LPMA)

  • Caroline Hillairet

    (CMAP)

  • Mohamed Mrad

    (LAGA)

Abstract

The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long maturity modelization, the possibility of adjusting preferences to new economic information is crucial. Thus, after recalling some important properties on progressive utility, this paper first provides an extension of the notion of a consistent progressive utility to a consistent pair of progressive utilities of investment and consumption. An optimality condition is that the utility from the wealth satisfies a second order SPDE of HJB type involving the Fenchel-Legendre transform of the utility from consumption. This SPDE is solved in order to give a full characterization of this class of consistent progressive pair of utilities. An application of this results is to revisit the classical backward optimization problem in the light of progressive utility theory, emphasizing intertemporal-consistency issue. Then we study the dynamics of the marginal utility yield curve, and give example with backward and progressive power utilities.

Suggested Citation

  • Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    • Handle: RePEc:arx:papers:1404.1895
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    References listed on IDEAS

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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Affine long term yield curves: An application of the Ramsey rule with progressive utility," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-24.
    3. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    4. Gollier, Christian, 2010. "Expected net present value, expected net future value, and the Ramsey rule," Journal of Environmental Economics and Management, Elsevier, vol. 59(2), pages 142-148, March.
    5. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    6. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    7. Martin L. Weitzman, 2007. "A Review of the Stern Review on the Economics of Climate Change," Journal of Economic Literature, American Economic Association, vol. 45(3), pages 703-724, September.
    8. Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 3, pages 1-14.
    9. Stern,Nicholas, 2007. "The Economics of Climate Change," Cambridge Books, Cambridge University Press, number 9780521700801.
    10. Nicole El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Working Papers hal-00477380, HAL.
    11. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    12. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    13. Weitzman, Martin L., 1998. "Why the Far-Distant Future Should Be Discounted at Its Lowest Possible Rate," Journal of Environmental Economics and Management, Elsevier, vol. 36(3), pages 201-208, November.
    14. Dybvig, Philip H & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1996. "Long Forward and Zero-Coupon Rates Can Never Fall," The Journal of Business, University of Chicago Press, vol. 69(1), pages 1-25, January.
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    Cited by:

    1. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2022. "Ramsey rule with forward/backward utility for long-term yield curves modeling," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 375-414, June.
    2. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Affine long term yield curves: An application of the Ramsey rule with progressive utility," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-24.
    3. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Post-Print hal-01728554, HAL.
    4. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    5. Bensusan, Harry & El Karoui, Nicole & Loisel, Stéphane & Salhi, Yahia, 2016. "Partial splitting of longevity and financial risks: The longevity nominal choosing swaptions," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 61-72.
    6. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2019. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Post-Print hal-01721441, HAL.
    7. Edouard Debonneuil & Anne Eyraud-Loisel & Frédéric Planchet, 2018. "Can Pension Funds Partially Manage Longevity Risk by Investing in a Longevity Megafund?," Risks, MDPI, vol. 6(3), pages 1-27, July.
    8. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    9. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Post-Print hal-00974831, HAL.
    10. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad & El Karoui & Hillairet Caroline & Mrad Mohamed, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
    11. Mrad Mohamed, 2020. "Mixture of consistent stochastic utilities, and a priori randomness," Working Papers hal-01728554, HAL.
    12. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Construction of an aggregate consistent utility, without Pareto optimality. Application to Long-Term yield curve Modeling," Working Papers hal-01721441, HAL.

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