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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)

  • Caroline Hillairet

    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - X - École polytechnique - 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)

  • El Karoui
  • Hillairet Caroline
  • Mrad Mohamed

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 & El Karoui & Hillairet Caroline & Mrad Mohamed, 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
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    References listed on IDEAS

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    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

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