Subject
Mathematics
Program
Master of Science (MSc)
Location
Côte-des-Neiges
Instruction mode
Credits
3
Description
This course covers the main tools of probability theory that are used in finance and financial engineering. Besides the theoretical concepts and proofs, many applications in finance are presented rigorously.
The first half of the course is in discrete time, while the second half is about continuous time models. For each of these two parts, there is a theoretical component in which the basic concepts such as martingales, stochastic integrals and diffusion processes are introduced and a more applied segment where the mathematical tools are applied to financial problems.
Themes covered
Mathematical background in probability and measure theory on finite set.
Fundamental set sigma-fields probability measure random variable stochastic processes filtration stopping-time conditional expectation martingales.
Applications to finance
Arbitrage investment strategy contingent claims pricing risk neutral measure.
Explanation and proof of the main result of Harrison and Pliska (1984).
Continuous time mathematical background
Convergence of sequence of random variables Brownian motion solution to stochastic differential Equation Itô's lemma Radon-Nikodym derivative Girsanov theorem Martingale Representation Theorem.
Application to finance
Pricing in absence of arbitrage change of measures complete and incomplete market hedging.
Important notes
Course in French : MATH 60646
The PhD course MATH 80646A is now a MSc course