Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

Abstract

We study a modelization of long term yield curves. Inspired by the economic litterature, we provide a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate optimal consumption. For such a long term modelization, the possibility of adjusting preferences to new economic information is crucial, justifying the use of progressive utility. We first characterize consistent progressive utility of investment and consumption, given the optimal wealth and consumption processes. A special attention is paid to utilities associated with linear optimal processes with respect to their initial conditions, which is the case of power progressive utilities. We study the dynamics of the marginal utility yield curve, and give example with backward and progressive power utilities, in a case of a log-normal or affine markets. Joint work with Nicole El Karoui and Mohamed Mrad