Rational expectations models: An approach using forward–backward stochastic differential equations

We show that a general class of continuous time rational expectations models can be reformulated as forward–backward stochastic differential equations (FBSDEs). Using this connection we obtain results on the conditions under which paths leading to, or keeping close to equilibrium exist, as well as their qualitative properties. We also provide a method for the construction of such paths through the connection of FBSDEs with quasilinear partial differential equations (PDEs). The theory is applied to specific macroeconomic models.