Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling

Nicole El Karoui (1) , Caroline Hillairet (2) , Mohamed Mrad (3) , El Karoui , Hillairet Caroline , Mrad Mohamed

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: SDEs; stochastic utility with consumtion; Long term Yield curve; consistent stochastic utilities; forward utilities; Forward/backward portfolio optimization; Market-consistent progressive utility of investment and consumption; Marginal indifference pricing; Yields curves; Ramsey rule; stochastic flows; Utility SPDE; Long run rates; Forward/backward portfolio optimization JEL 2018: C54; C61; D52; E43; G12

Domaines: Finance quantitative [q-fin.CP]

Nicole El Karoui, Caroline Hillairet, Mohamed Mrad, El Karoui, Hillairet Caroline, et al.. Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling. Decisions in Economics and Finance, 2020. ⟨hal-00974815v3⟩