Diffusions, financial asset prices, interest rates and consumption: the case of intertemporally dependent preferences.

Summary This work is situated in the framework of the general diffusion equilibrium. We recall in the first chapter the immense richness of the relations obtained in this framework, in order to underline that the results are very closely linked to the modeling of the chosen behavior. The current trend in this area of economics and finance is to move towards greater finesse in the modeling of utility functions, in order to obtain results consistent with the observed macroeconomic series, which are currently poorly explained by the models. The aim of this work is to examine the impact of the relaxation of an assumption long used even implicitly in the models, called additivity or separability of the utility function. We shall see in the first chapter that the relaxation of this intuitively very questionable hypothesis destroys the condition of the classical envelope, which allows us, even in the simple model of Merton (1969), to find results that are more consistent with empirical tests: consumption is no longer proportional to wealth with a constant factor (Sundaresan (1990)). In the remaining chapters, we examine how this result can be extended to the most general economy possible. The first step in our approach, which corresponds to chapter 2, is to identify the extent to which the very general results of the Cox, Ingersoll et al.