Abstracts

For financing of ecological projects reducing global warming, for longevity issues or any other investment with a long term impact, it is necessary to model accurately long run interest rates. The answer cannot find in financial market, since for longer maturities, the bond market becomes highly illiquid and standard financial interest rates models cannot be easily extended. In general, these issues are addressed at macroeconomic level, where long-run interest rates has not necessary the same meaning than in financial market.They are called socially efficient or economic interest rates, because they would be only affected by structural characteristics of the economy, and to be low-sensitive to monetary policy.
The macroeconomics literature typically relates the economic equilibrium rate to the time preference rate and to the average rate of productivity growth. A typical example is the Ramsey rule. In our financial point of view, the representative agent may invest in a financial market in addition to the money market. We consider an arbitrage approach with exogenously given interest rate, instead of an equilibrium approach that determines them endogenously.
In a first step, considering a classical portfolio optimization, we give a financial interpretation of the equilibrium yield curve given by the Ramsey Rule. In a second step, we introduce dynamic utility functions that allow to get rid of the dependency on the maturity of the classical backward optimization problem and thus gives time consistency for the optimal choices. Besides, as dynamic utility functions take into account that the preferences and risk aversion of investor may change with time, they are also more accurate. Indeed, in the presence of generalized long term uncertainty, the decision scheme must evolve. Finally, to give more precise properties of the marginal utility yield curve, we study forward and backward power utilities, in the example of log-normal market and affine market.