EP30.FSF1104 — Stochastic Calculus

This course provides a rigorous introduction to stochastic calculus, focusing on continuous-time models essential for advanced quantitative analysis in finance, engineering, and science. Building upon general probability theory, the course develops the mathematics of Brownian motion, the Itô integral, and Stochastic Differential Equations (SDEs). Key theoretical topics include the Ito formula, Girsanov’s theorem, martingale representation, and the connection between SDEs and Partial Differential Equations (Feynman-Kac theorem). The course emphasizes applications, particularly the risk-neutral pricing framework (Black-Scholes-Merton) and diffusion models in finance.

Requirements for Final Examination

Attendance score must be at least 5 (according to University regulations).

See Appendix 2, Rubric 1 for attendance evaluation.

Requirements for Class Attendance

Students are responsible for attending all scheduled classes.

In case of absence due to force majeure, students must actively acquire the knowledge through the materials provided by the lecturer and other assigned readings.

Requirements for In-class Behaviour

The course is conducted on the principle of mutual respect between lecturers and students.

Students are required to take full notes and participate in answering questions.

Students must read assigned materials in advance.

Homework assignments must be completed as required.

Students must not make noise and disturb others.

Laptops, tablets, and mobile phones may only be used for note-taking, calculations, or learning purposes, and must not be used for any other activities.

The course content includes

• General Probability Theory
• Brownian Motion
• Stochastic Integration
• Stochastic Differential Equations
• Connections with Partial Differential Equations
• Change of measure and Girsanov theorem
• Applications in Finance