Modelli decisionali stocastici

The current dissertation is focused on the construction of stochastic decision models (or simply decision model) with discrete time and on their applications to stochastic control. Mathematical theory of discrete time decision processes has been originated by R. Bellman and by A. Wald. It has now a large number of applications in almost all branches of natural sciences (biology, mathematical finance,¿). It is known in engineering as stochastic control. We prove several theorems and results aimed to solve the control problems based on the decision models. In particular, we extend parts of the interesting monograph written by J. Zabczyk, providing also some quite involving proofs which are not given by the author. We arrive to solve the portfolio problem which is much used in financial mathematics.