Modelling: Continuous state space -- discrete time

In the previous chapter we investigated models where the state space $\Omega$ consists of a finite number of elements, and the time evolves in a discrete way. Now we will consider cases where the state space is continuous. Such models are very hard to theoretically manipulate, one will find out that markets are by construction incomplete. On the other hand, these are the only markets for which econometric procedures for the estimation of the parameters have been developed and tested extensively over the years. Therefore one finds herself in a position where the models that can easily be implemented from an empirical [econometric] point of view are the most cumbersome for one to deal with from a theoretical [derivative pricing] point of view.