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Mathematical Finance
Last Updated: 2026-02-05 16:30:05
Abstract
Advanced course on mathematical finance:- semimartingales and general stochastic integration- absence of arbitrage and martingale measures- fundamental theorem of asset pricing- option pricing and hedging- hedging duality- optimal investment problems- additional topics
Objective
Advanced course on mathematical finance, presupposing good knowledge in probability theory and stochastic calculus (for continuous processes)
Content
This is an advanced course on mathematical finance for students with a good background in probability. We want to give an overview of main concepts, questions and approaches, and we do this mostly in continuous-time models. Topics include - semimartingales and general stochastic integration - absence of arbitrage and martingale measures - fundamental theorem of asset pricing - option pricing and hedging - hedging duality - optimal investment problems - and probably others
Resources
Lecture Notes
The course is based on different parts from different books as well as on original research literature.Lecture notes will not be available.
Literature
While there are many textbooks on mathematical finance, none of them is ideal to cover the contents of this course. References include the following books: - T. Björk, Arbitrage Theory in Continuous Time, 4th edition, Oxford Academic (2019) - J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, MIT Press (2004) - F. Delbaen and W. Schachermayer, The Mathematics of Arbitrage, Springer (2006) - E. Eberlein and J. Kallsen, Mathematical Finance, Springer (2019) - R. J. Elliott and E. P. Kopp, Mathematics of Financial Markets, 2nd edition, Springer (2005) - P. Hunt and J. Kennedy, Financial Derivatives in Theory and Practice, revised edition, Wiley (2004) - M. Jeanblanc, M. Yor and M. Chesney, Mathematical Methods for Financial Markets, Springer (2009) - G. Kallianpur and R. L. Karandikar, Introduction to Option Pricing Theory, Springer (2000) - I. Karatzas and C. Kardaras, Portfolio Theory and Arbitrage: A Course in Mathematical Finance, American Mathematical Society (2021) - I. Karatzas and S. E. Shreve, Methods of Mathematical Finance, Springer (1998) - D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, 2nd edition, CRC Press (2007) - A. N. Shiryaev, Essentials of Stochastic Finance: Facts, Models, Theory, World Scientific (1999)
Learning Materials (Links)
- Main link
- Information
General Information
- Language
- English
- Levels
- MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 30 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture | Mathematical Finance |
|
4 h weekly |
| exercise | Mathematical Finance |
|
2 h weekly |
Offered In
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Core Courses (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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Quantitative Finance Master (see Students in the Joint Degree Master's Programme "Quantitative Finance" must book University of Zurich modules directly at the University of Zurich. Those modules are not listed here.)
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MF (Mathematical Methods in Finance) (For possible additional course offerings see )
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