IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-00974815.html
   My bibliography  Save this paper

Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

Author

Listed:
  • Nicole El Karoui

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique)

  • Mohamed Mrad

    (LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique)

  • Caroline Hillairet

    (ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique)

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 & Mohamed Mrad & Caroline Hillairet, 2020. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Post-Print hal-00974815, HAL.
    • Handle: RePEc:hal:journl:hal-00974815
    Note: View the original document on HAL open archive server: https://hal.science/hal-00974815v3
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00974815v3/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dumas, Bernard & Luciano, Elisa, 2017. "The Economics of Continuous-Time Finance," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262036541, April.
    2. Christian Gollier, 2012. "Pricing the Planet's Future: The Economics of Discounting in an Uncertain World," Economics Books, Princeton University Press, edition 1, volume 1, number 9894.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    4. 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.
    5. Jaksa Cvitanic & Elyès Jouini & Semyon Malamud & Clotilde Napp, 2011. "Financial Markets Equilibrium with Heterogeneous Agents," Review of Finance, European Finance Association, vol. 16(1), pages 285-321.
    6. 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.
    7. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    8. Damir Filipović & Eckhard Platen, 2009. "Consistent Market Extensions Under The Benchmark Approach," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 41-52, January.
    9. 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.
    10. Nicole El Karoui & Mohamed Mrad, 2013. "An Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE," Post-Print hal-00477381, HAL.
    11. He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
    12. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2018. "Consistent Utility of Investment and Consumption : a forward/backward SPDE viewpoint ," Post-Print hal-01458419, HAL.
    13. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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 & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Papers 1404.1913, arXiv.org.
    3. 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.
    4. Nicole El Karoui & Caroline Hillairet & Mohamed Mrad, 2014. "Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling," Papers 1404.1895, arXiv.org.
    5. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Working Papers hal-00974831, HAL.
    6. Nicole El Karoui & Mohamed Mrad & Caroline Hillairet, 2014. "Ramsey Rule with Progressive utility and Long Term Affine Yields Curves," Post-Print hal-00974831, HAL.
    7. J. Doyne Farmer & John Geanakoplos & Matteo G. Richiardi & Miquel Montero & Josep Perelló & Jaume Masoliver, 2024. "Discounting the Distant Future: What Do Historical Bond Prices Imply about the Long-Term Discount Rate?," Mathematics, MDPI, vol. 12(5), pages 1-25, February.
    8. Fleurbaey, Marc & Zuber, Stéphane, 2015. "Discounting, risk and inequality: A general approach," Journal of Public Economics, Elsevier, vol. 128(C), pages 34-49.
    9. Kollenberg, Sascha & Taschini, Luca, 2016. "Emissions trading systems with cap adjustments," Journal of Environmental Economics and Management, Elsevier, vol. 80(C), pages 20-36.
    10. Lutz Kruschwitz, 2018. "Das Problem der Anschlussverzinsung," Schmalenbach Journal of Business Research, Springer, vol. 70(1), pages 9-45, March.
    11. Olijslagers, Stan & van der Ploeg, Frederick & van Wijnbergen, Sweder, 2023. "On current and future carbon prices in a risky world," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    12. Jouini, Elyès & Marin, Jean-Michel & Napp, Clotilde, 2010. "Discounting and divergence of opinion," Journal of Economic Theory, Elsevier, vol. 145(2), pages 830-859, March.
    13. 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.
    14. Wolfgang Buchholz, 2014. "Discounting in an Uncertain World - Disentangling the Debate on the Weitzman-Gollier Puzzle," CESifo Working Paper Series 4967, CESifo.
    15. Davidson, Marc D., 2014. "Zero discounting can compensate future generations for climate damage," Ecological Economics, Elsevier, vol. 105(C), pages 40-47.
    16. Antony Millner, 2016. "Heterogeneous intergenerational altruism," GRI Working Papers 226, Grantham Research Institute on Climate Change and the Environment.
    17. Antony Millner & Geoffrey Heal, 2015. "Collective intertemporal choice: time consistency vs. time invariance," GRI Working Papers 220, Grantham Research Institute on Climate Change and the Environment.
    18. Jouini, Elyès & Napp, Clotilde, 2014. "How to aggregate experts' discount rates: An equilibrium approach," Economic Modelling, Elsevier, vol. 36(C), pages 235-243.
    19. J. Doyne Farmer & John Geanakoplos & Jaume Masoliver & Miquel Montero & Josep Perello, 2014. "Discounting the Distant Future," Cowles Foundation Discussion Papers 1951, Cowles Foundation for Research in Economics, Yale University.
    20. Moritz Drupp & Mark Freeman & Ben Groom & Frikk Nesje, 2015. "Discounting disentangled: an expert survey on the determinants of the long-term social discount rate," GRI Working Papers 196a, Grantham Research Institute on Climate Change and the Environment.

    More about this item

    Keywords

    SDEs; stochastic utility with consumtion; Long term Yield curve; consistent stochastic utilities; forward utilities; Forward/backward portfolio optimization; Market-consistent progressive utility of investment and consumption; Marginal indifference pricing; Yields curves; Ramsey rule; stochastic flows; Utility SPDE; Long run rates; Forward/backward portfolio optimization JEL 2018: C54; C61; D52; E43; G12;
    All these keywords.

    JEL classification:

    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00974815. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.