Statistics, Finance and Actuarial sciences

Knowledge and understanding. Students who have attended the course of stochastic processes will have a general understanding of the modern theory of stochastic processes including point processes, martingales, stochastic calculus with respect to the Brownian motion. Some parts of the program have an advanced character and involve fractional Brownian motion and the interplay between partial differential equations and diffusion processes. Ability of applying knowledge and understanding. The part of the course concerning stochastic calculus make the students capable of applying the concepts and techniques to the main models of finance (Black and Scholes, Vasichek and others). The Feynman-Kac functional permits the students to have at hand a flexible and powerful tool for many specific situations. Autonomous judgement. The course is presented with the aim of inserting the subject in the framework of modelling random phenomena in finance, economics and physics. Each part of the program is presented both on an intuitive and rigorous basis letting the student foresee further developments. Communication skills. The study of many probabilistic concepts and techniques gives the possibility of acquiring a rigorous terminology and a method of proving results according to the scheme assumption, proof, conclusion, interpretation of the results. Learning skills. The style of lesson is such that the student must learn to learn new concepts and acquire new knowledge and it aims at stimulating the curiosity about all possible applications and interactions between scientific fields.