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Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

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Author Info

  • Nicole El Karoui

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Pierre et Marie Curie (UPMC) - Paris VI - Université Paris VII - Paris Diderot)

  • Caroline Hillairet

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

  • Mohamed Mrad

    ()
    (LAGA - Laboratoire Analyse, Géométrie et Applications - CNRS : UMR7539 - Université Paris 13 - Université Paris VIII - Vincennes Saint-Denis - Institut Galilée - Université Sorbonne Paris Cité (USPC))

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    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.

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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00974815.

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    Date of creation: 07 Apr 2014
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    Handle: RePEc:hal:wpaper:hal-00974815

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00974815
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    Related research

    Keywords: forward utilities; consistent stochastic utilities; stochastic utility with consumtion; Ramsey Rule; Long term Yield curve; SDEs; Utility SPDE; stochastic flows;

    This paper has been announced in the following NEP Reports:

    References

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    1. 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.
    2. Gollier, Christian, 2009. "Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule," IDEI Working Papers, Institut d'Économie Industrielle (IDEI), Toulouse 557, Institut d'Économie Industrielle (IDEI), Toulouse.
    3. Damir Filipovic & Eckhard Platen, 2007. "Consistent Market Extensions under the Benchmark Approach," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 189, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    5. N. El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Working Papers hal-00477380, HAL.
    6. Gollier, Christian, 2009. "Should We Discount the Far-Distant Future at Its Lowest Possible Rate?," Economics Discussion Papers 2009-7, Kiel Institute for the World Economy.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
    8. 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.
    9. Jonathan E. Ingersoll Jr. & Philip H. Dybvig & Stephen A. Ross, 1998. "Long Forward and Zero-Coupon Rates Can Never Fall," Yale School of Management Working Papers, Yale School of Management ysm45, Yale School of Management.
    10. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
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    Cited by:
    1. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    2. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.

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