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,...

We consider a Markov switching regime and price a discount bond using two popular models for the short rate, the Vasicek- and CIR-dynamics. In both cases, an explicit formula is obtained for the bond price which includes the solution of a matrix ODE. Our model is easy to calculate and captures...

Motivated by the work of Musiela and Zariphopoulou \cite{zar-03}, we study the Itô random fields which are utility functions $U(t,x)$ for any $(\omega,t)$. The main tool is the marginal utility $U_x(t,x)$ and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate...