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MTHE 437 Topics In Applied Mathematics Units: 3.50
Topic: An Introduction to Stochastic Differential Equations (with Applications to Mathematical Finance and Engineering)
The aim of this course is to provide a rigorous introduction to the theory of stochastic calculus and stochastic differential equations, and to survey some of its most important applications, especially in Mathematical Finance. The Ito stochastic integral and its associated Ito Calculus will be derived in the general framework of continuous semimartingales, leading to a detailed treatment of stochastic differential equations (SDEs) and their properties. The theory thus developed will be applied to selected problems in Mathematical Finance (option pricing and hedging, trading strategies and arbitrage) and Engineering (boundary-value problems, filtering, optimal control). Numerical aspects of SDEs will also be discussed.
DELETED 2025-2026.
(Lec: 3, Lab: 0, Tut: 0.5)
The aim of this course is to provide a rigorous introduction to the theory of stochastic calculus and stochastic differential equations, and to survey some of its most important applications, especially in Mathematical Finance. The Ito stochastic integral and its associated Ito Calculus will be derived in the general framework of continuous semimartingales, leading to a detailed treatment of stochastic differential equations (SDEs) and their properties. The theory thus developed will be applied to selected problems in Mathematical Finance (option pricing and hedging, trading strategies and arbitrage) and Engineering (boundary-value problems, filtering, optimal control). Numerical aspects of SDEs will also be discussed.
DELETED 2025-2026.
(Lec: 3, Lab: 0, Tut: 0.5)
Requirements: Prerequisites: MTHE 328 and MTHE 351, or permission of the instructor
Corequisites:
Exclusions:
Offering Term: W
CEAB Units:
Mathematics 18
Natural Sciences 0
Complementary Studies 0
Engineering Science 12
Engineering Design 12
Offering Faculty: Faculty of Arts and Science
Course Learning Outcomes:
- Using the Ito calculus in the study of stochastic processes.
- Determining (local) martingale properties of stochastic processes defined through stochastic integration.
- Rigorous understanding of Brownian motion and its main properties.
- Rigorous understanding of the Ito stochastic integral and its properties.
- Rigorously using results from martingale theory in establishing properties of stochastic processes.
- Using tools from stochastic analysis in the study of uniformly elliptic partial differential equations.