Lecturer

Prof. Dr. Beatrice Acciaio

Coordinator

Chiara Rossato

Lectures

Thursday	8:15-10	ML F 39
Friday	8:15-10	HG D 3.2

Exercise Classes

The first exercise class is on September 27, during the second week of the semester.

Friday

10:15-12

ML F 39

Important information for the last weeks:

• The lectures and exercise classes will finish on Friday, 13th December.

Course organisation

Lectures and exercise classes are scheduled to be in-person (except if explicitly stated otherwise). There will be no recordings.

The course is based on different parts from different books, as well as on original research literature. There are no lecture notes for this course. However, notes written by the lecturer in class are available here.

Course Catalogue

401-4889-00L Mathematical Finance

Exam

The grade for this course is based solely on the final exam. The exam is oral, 30 minutes (no preparation time) and will cover all the material discussed during the lectures and all the material from the exercise sheets (except if explicitly stated otherwise).

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 to be covered 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

Prerequisites

Prerequisites are the standard courses

• Probability Theory
• Brownian Motion and Stochastic Calculus (for which lecture notes are available here)

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), 401-3888-00L, 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.

Office hours

The assistants of Group 3 (Probability Theory, Insurance Mathematics and Stochastic Finance) offer regular office hours for questions on courses and exercise classes taught by the professors in the group. Click here for more information. Note that you can also ask questions during the exercise classes.

Exercises

New exercise sheets are uploaded below on Wednesdays before the corresponding Friday exercise class, along with solutions to the exercise sheet from the previous week.

Even though it is not compulsory, you are strongly encouraged to solve the exercises and hand in your solutions. This can be done electronically. Please follow the instructions below.

1. Scan your solution into a single PDF file
2. Name the created file as {email address}_{exercise sheet number}.pdf (e.g. andrey.kolmogorov@probability.com_1.pdf)
3. Upload your solution using the button below before 12:00 on the indicated Wednesday. The password will be emailed to the enrolled students

Late submissions will not be considered.

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)