Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling
Nicole El Karoui,
Caroline Hillairet and
Mohamed Mrad ()
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Nicole El Karoui: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UP7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Caroline Hillairet: CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique
Mohamed Mrad: LAGA - Laboratoire Analyse, Géométrie et Applications - CNRS - Centre National de la Recherche Scientifique - UP8 - Université Paris 8, Vincennes-Saint-Denis - Université Paris 13 - Université Sorbonne Paris Cité (USPC) - Institut Galilée
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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.
Keywords: forward utilities; consistent stochastic utilities; stochastic utility with consumtion; Ramsey Rule; Long term Yield curve; SDEs; Utility SPDE; stochastic flows (search for similar items in EconPapers)
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