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Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

  • Nicole El Karoui


  • Mohamed Mrad


  • Caroline Hillairet


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    The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, 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, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.

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    Paper provided by in its series Papers with number 1404.1913.

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    Date of creation: Apr 2014
    Date of revision:
    Handle: RePEc:arx:papers:1404.1913
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    1. 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.
    2. N. El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Working Papers hal-00477380, HAL.
    3. GOLLIER Christian, 2008. "Should we discount the far-distant future at its lowest possible rate?," LERNA Working Papers 08.30.274, LERNA, University of Toulouse.
    4. 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.
    5. 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.
    6. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895,
    7. 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.
    8. David Bolder & Shudan Liu, 2007. "Examining Simple Joint Macroeconomic and Term-Structure Models: A Practitioner's Perspective," Working Papers 07-49, Bank of Canada.
    9. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Working Papers hal-00974815, HAL.
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