Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

TL;DR

This paper models long-term affine yield curves using the Ramsey rule and progressive utility, emphasizing the impact of initial wealth and preferences adjustments on yield curve dynamics.

Contribution

It introduces a framework combining the Ramsey rule with progressive utility in affine models, characterizing consistent utilities and analyzing initial wealth effects on yield curves.

Findings

Characterization of consistent progressive utilities in affine models

Analysis of utilities with linear optimal processes

Impact of initial wealth on yield curve shape

Abstract

The purpose of this paper relies on the study of long term affine yield curves modeling. It is inspired by the Ramsey rule of the economic literature, 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, justifying the use of progressive utility. This paper studies, in a framework with affine factors, the yield curve given from the Ramsey rule. It first characterizes 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 for example the case of power progressive utilities. Those utilities are the basis point to construct other progressive utilities generating non linear optimal processes but leading yet to still tractable computations. This is of particular interest to study the impact of initial wealth on yield curves.