401-4889-DRL Mathematical Finance
| Semester | Autumn Semester 2023 |
| Lecturers | M. Schweizer |
| Periodicity | yearly recurring course |
| Language of instruction | English |
| Comment | Only for ZGSM (ETH D-MATH and UZH I-MATH) doctoral students. The latter need to register at myStudies and then send an email to info@zgsm.ch with their name, course number and student ID. Please see https://zgsm.math.uzh.ch/index.php?id=forum0 |
| 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 | |||||||||||||||||||||||||||||||||
| Learning 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 | |||||||||||||||||||||||||||||||||
| 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) | |||||||||||||||||||||||||||||||||
| Prerequisites / Notice | Prerequisites are the standard courses - Probability Theory (for which lecture notes are available) - Brownian Motion and Stochastic Calculus (for which lecture notes are available) Those students who already attended "Introduction to Mathematical Finance" will have an advantage in terms of ideas and concepts. This course is the second of a sequence of two courses on mathematical finance. The first course "Introduction to Mathematical Finance" (MF I), 401-3888-00, focuses on models in finite discrete time. It is advisable that the course MF I is taken prior to the present course, MF II. For an overview of courses offered in the area of mathematical finance, see Link. | |||||||||||||||||||||||||||||||||
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