Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling
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.
|Date of creation:||07 Apr 2014|
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- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
- Eckhard Platen, 2004.
"A Benchmark Approach to Finance,"
Research Paper Series
138, Quantitative Finance Research Centre, University of Technology, Sydney.
- Gollier, Christian, 2009.
"Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule,"
IDEI Working Papers
557, Institut d'Économie Industrielle (IDEI), Toulouse.
- 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.
- GOLLIER Christian, 2008. "Expected net present value, expected net future value, and the Ramsey rule," LERNA Working Papers 08.29.273, LERNA, University of Toulouse.
- Gollier, Christian, 2009. "Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule," TSE Working Papers 09-049, Toulouse School of Economics (TSE).
- Christian Gollier, 2009. "Expected Net Present Value, Expected Net Future Value, and the Ramsey Rule," CESifo Working Paper Series 2643, CESifo Group Munich.
- 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.
- 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
ysm45, Yale School of Management.
- Damir Filipovic & Eckhard Platen, 2007.
"Consistent Market Extensions under the Benchmark Approach,"
Research Paper Series
189, Quantitative Finance Research Centre, University of Technology, Sydney.
- Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52.
- 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.
- Gollier, Christian, 2009. "Should we Discount the Far-Distant Future at its Lowest Possible Rate?," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 3, pages 1-14.
- 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.
- N. El Karoui & Mohamed M'Rad, 2010. "Stochastic Utilities With a Given Optimal Portfolio : Approach by Stochastic Flows," Working Papers hal-00477380, HAL.
- Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
- 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.
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