401-4889-DRL  Mathematical Finance

Courses

Catalogue data

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.
Competencies	Subject-specific Competencies Concepts and Theories assessed Method-specific Competencies Analytical Competencies assessed Decision-making fostered Problem-solving assessed Social Competencies Communication assessed Cooperation and Teamwork fostered Leadership and Responsibility fostered Personal Competencies Adaptability and Flexibility fostered Creative Thinking assessed Critical Thinking assessed Integrity and Work Ethics fostered

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits	3 credits
Examiners	M. Schweizer
Type	ungraded semester performance
Language of examination	English
Repetition	Repetition only possible after re-enrolling for the course unit.
Admission requirement	Credit points for doctoral students will be given subject to some conditions. These will be announced later upon request.
Additional information on mode of examination	Credit points for doctoral students will be given subject to some conditions. These will be announced later upon request.

Learning materials

Groups

Restrictions

Offered in

Programme	Section	Type
Doctorate Mathematics	Graduate School	W