MF0 Stochastic integrals: an introduction to the Itō calculus
Lecturer: Dr. Eyal Neuman, Imperial
Time and dates: Mondays 4pm-7pm. The first lecture is on Jan 22nd.
Location: Huxley 130, department of Mathematics, Imperial College.
Knowledge of measure theory, probability theory and martingales is assumed as a prerequisite.
This course is an introduction to the Ito calculus, a calculus applicable to functions of stochastic processes with irregular paths, which has many applications in finance, engineering and physics. The course shall focus on the mathematical foundations of stochastic calculus and the theory of stochastic integration, using a less conventional approach which emphasizes pathwise, rather than probabilistic, methods.
The first part of the course will focus on pathwise integration with respect to functions of finite quadratic variation, without using any probabilistic tools.
The second part of the course will explore the application of these results to stochastic integrations with respect to semimartingales, a setting which covers most examples of stochastic processes of interest in applications - including jump processes and diffusion processes.
Stochastic Integration and Differential Equations, by Philip E. Protter