Ramsey Rule with Progressive utility and Long Term Affine Yields Curves

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

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 LAGA - Laboratoire Analyse, Géométrie et Applications
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

he 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.

Mots clés: affine yields curves; Progressive utility with consumption; market consistency; portfolio optimization; Ramsey rule; affine yields curves.

Domaines: Finance quantitative [q-fin.CP]

Nicole El Karoui, Mohamed Mrad, Caroline Hillairet. Ramsey Rule with Progressive utility and Long Term Affine Yields Curves. International Journal of Financial Engineering, 2014. ⟨hal-00974831⟩