Ramsey Rule with Progressive Utility in Long Term Yield Curves Modeling
Résumé
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]Origine | Fichiers produits par l'(les) auteur(s) |
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