Κίνηση Brown και το μοντέλο Black-Scholes
Brown motion and the Black-Scholes model
KeywordsΚίνηση Brown ; Στοχαστικές διαδικασίες ; Στοχαστικός λογισμός ; Χρηματοοικονομική ; Μοντέλο Black Scholes ; Martingales
First of all, is presented a systematic study of Brownian motion. The first problem one encounters with Brownian motion is its existence. One approach to this question is to write down what the finite-dimensional distributions of this process must be, and then to construct a probability measure and a process on an appropriate measurable space in such a way that we obtain the prescribed finite-dimensional distributions. A more elegant approach for Brownian motion is close in spirit to Wiener’s (1923) original construction, which was modified by Levy (1948) and later further simplified by Ciesielski (1961). Finally, the Black-Scholes model is analyzed as an application of Brownian motion.