# Stochastic Calculus (2019-2020)

2019-2020

Lecturer(s):

Prof. Hanqing Jin

Course Term:

Michaelmas

Course Overview:

Stochastic differential equations are used to model the behaviour of financial assets and stochastic calculus is the fundamental tool for understanding and manipulating these models. This course will give an introduction to the main ideas in stocahstic calculus that will be used through out the MSc programme.

Course Syllabus:

Introduction to Brownian motion, continuous martingales and their properties, distribution of first hitting times, maximum and minimum, for Brownian motion. Ito's calculus: quadratic variation, stochastic

integrals, Ito's formula, exponential martingales, Girsanov's theorem, the martingale representation theorem. Stochastic differential equations: weak and strong solutions, existence and uniqueness of solutions.