Ramsey rule with forward/backward utility for long-term yield curves modeling

Abstract

This paper draws a parallel between the economic and financial points of view in the modeling of long-term yield curves and provides new results on asymptotic long rates. The Ramsey rule, which is the reference equation in the economic literature to compute long-term discount rates, links endogenous discount rate and marginal utility of aggregate optimal consumption at equilibrium. This paper proposes a unified framework and a financial interpretation of the economic discount rate given by the Ramsey rule, using marginal utility indifference prices for non-replicable zero-coupon bonds. Optimal discounted pricing kernel is at the core of this unifying approach and is determined through an optimization program that can be posed backward or forward. The dynamics and the long-term behavior of the marginal utility yield curve is studied in both settings. Special attention is paid to its dependency on the initial wealth of the economy, as well as on the time-horizon in the backward setting, extending previous results in the literature.