2026/2027
Research Seminar "Stochastic Analysis and Applications in Finance"
ID 1249947
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Open to:
students of all HSE University campuses
Instructors:
Cedric Bernardin
Language:
English
ECTS credits:
3
Contact hours:
30
Course Syllabus
Abstract
This master-level course provides a rigorous introduction to the foundational tools of stochastic analysis and their direct applications in quantitative finance. Beginning with the theory of continuous-time stochastic processes, the curriculum develops the core concepts of martingales, Brownian motion, and Itô calculus. A central focus is placed on the formulation and solution of stochastic differential equations (SDEs), which serve as the fundamental models for asset prices, interest rates, and other key financial variables. The theoretical framework is then applied to core problems in financial engineering, including the derivation of the Black-Scholes partial differential equation, risk-neutral valuation, and the pricing of derivative securities. Advanced topics, such as the Feynman-Kac representation, stochastic optimal control, and an introduction to jump processes, may also be explored to equip students with the sophisticated mathematical toolkit required for modern quantitative risk management and asset pricing.
Learning Objectives
- Study objectives: This course provides a rigorous introduction to the foundational tools of stochastic analysis and their direct applications in quantitative finance.
Course Contents
- Filtrations, Stopping times and Continuous time martingales
- Continuous time Markov Processes
- Brownian motion and few properties
- Stochastic integral
- Itô’s formula, Girsanov’s theorem and consequences
- Stochastic Differential equations
- Financial applications: Black-Scholes model and beyond
Interim Assessment
- 2026/2027 2nd module0.1S+0.4M+0.5F, where S is the grade for participation, M is the midterm exam grade (written exam), F is the final exam grade (oral exam).
Bibliography
Recommended Core Bibliography
- Brownian motion and stochastic calculus, Karatzas, I., 1998
- Continuous Martingales and Brownian motion, Revuz, D., 1999
- Introduction to stochastic calculus applied to finance, Lamberton, D. M., 2008
Recommended Additional Bibliography
- Markov chains, Revuz, D., 2005