Credits: 9

Type: advanced and professional

Objectives:

Introduction to the basic tools of stochastic calculus and some applications for the modelling of random dynamical systems.

Knowledge:

Brownian motion and related processes. The Itô integral. Extensions. The Itô formula. The Stratanovich integral. The integral representation of martingales. The Girsanov theorem. Stochastic diferential equations. Applications.

Subject-specific competences:

• To show an understanding of the principle of Itô calculus and the Itô formula as a variable change formula for problem solving.
• To be able to gauge the effect of the change of probability measures in the space of paths, and to resolve elementary stochastic differential equations and understand their importance in different applications.
• To be able to obtain the Black-Scholes formula.