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401-4889-DRL 3 Credits DR D-MATH

Mathematical Finance

Lecturers & Examiners: Prof. Dr. Martin Schweizer
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 with their name, course number and student ID. Please see
VVZ CR n/a

Last Updated: 2026-02-05 16:14:50

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)

General Information

Language
English
Levels
DR
Frequency
Yearly recurring

Examination

Type
ungraded semester performance
Credit points for doctoral students will be given subject to some conditions. These will be announced later upon request.

Registration & Places

Priority: Registration for the course unit is only possible for the primary target group

Course Components

Type Title Time & Place Hours
lecture Mathematical Finance
  • Tue 08:15-10:00 (HG E 1.1)
  • Thu 08:15-10:00 (ML F 36)
4 h weekly
exercise Mathematical Finance
  • Fri 10:15-12:00 (ML F 38)
2 h weekly

Offered In