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The purpose of this paper relies on the study of long term yield curvesmodeling. Inspired by the economic litterature, it provides a financialinterpretation of the Ramsey rule that links discount rate and marginal utilityof aggregate optimal consumption. For such a long maturity modelization, thepossibility of adjusting preferences to new economic information is crucial.Thus, after recalling some important properties on progressive utility, thispaper first provides an extension of the notion of a consistent progressiveutility to a consistent pair of progressive utilities of investment andconsumption. An optimality condition is that the utility from the wealthsatisfies a second order SPDE of HJB type involving the Fenchel-Legendretransform of the utility from consumption. This SPDE is solved in order to givea full characterization of this class of consistent progressive pair ofutilities. An application of this results is to revisit the classical backwardoptimization problem in the light of progressive utility theory, emphasizingintertemporal-consistency issue. Then we study the dynamics of the marginalutility yield curve, and give example with backward and progressive powerutilities.

Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling