  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.
