Department of Mathematics

Mathematical Finance

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Lecturer Prof. H. Mete Soner

Lectures Tuesday




HG E 33.1

HG E 33.1

Matti Kiiski & Ren Liu
Problem sessions Friday
HG D 3.2

First lecture
Tuesday 15/09/2015
First exercise class
Friday 18/09/2015



Prof. H. Mete Soner

Office: HG G 54.3

Office Hours: by appointment


Problem Session:

Matti Kiiski & Ren Liu

Office: HG G 47.2

Office Hours: to be arranged



This course focuses on continuous time financial markets and requires a basic knowledge of measure theoretic probability theory and stochastic processes.


The tentative list of lectures are given below and provides a detailed list of the topics that will be covered.

Study material

For discrete time and general information the following books are useful.

For more about discrete time models, see last years course Introduction to Mathematical Finance.

Continuous time mathematical finance:

Lecture notes from 2011.

Lecture notes from 2013.

Supplementary material:

Stochastic calculus in a nutshell (by Martin Blais).

Lecture 7 notes

Lecture 14 was based on the survey article by Walter Schachermayer.

Lecture 23 was based on the article by Jaksa Cvitanic and Ioannis Karatzas.

The etymology of the word martingale.

Ex. 1-1 b) iii) solution details


Lecture Date

Introduction and Brief Summary of Discrete Time models
 2  17.09.2015
Financial markets and relevant concepts
 3  22.09.2015 Arbitrage and Martingale Measures
 4  24.09.2015 Fundamental Theorem of Asset Pricing
 5  29.09.2015 Black & Scholes Model
 6  01.10.2015 Options and Marginals
 7  06.10.2015
Convex Analysis and Fenchel-Moreau Theorem
 8  08.10.2015 Pricing and Hedging
 9  13.10.2015 American Options
 10  15.10.2015 Levy Processes
 11  20.10.2015 No Class
 12  22.10.2015
No Class
 13  27.10.2015 Heston Model
 14  29.10.2015 Utility maximization and duality
 15  03.11.2015 Stochastic Optimal Control - introduction
 16  05.11.2015 Merton Problem
 17  10.11.2015 Markets with Transaction Costs
 18  12.11.2015 Markets with Transaction Costs
 19  17.11.2015 Asymptotic methods
 20  19.11.2015 Asymptotic methods
 21  24.11.2015
Backward Stochastic Differential Equations (BSDE)
 22  26.11.2015 BSDE's and utility maximization
 23  01.12.2015 Risk measures
 24  03.12.2015 Risk measures and BSDE's
 25  08.12.2015 Interest rate theory
 26  10.12.2015 Interest rate theory
 27  15.12.2015 Interest rate theory
 28  17.12.2015 Interest rate theory

Exercise classes

We will provide bi-weekly homework assignments. Students are advised to study them in a timely manner. You will find the exercises here.

Assistant hour ("Präsenz")

There are regular assistant hours ("Präsenz") on Mondays and Thursdays, 12:00-13:00 in HG G 32.6.

Examination details

There will be a 30 minutes long oral examination at the end of the semester.


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© 2016 Mathematics Department | Imprint | Disclaimer | 1 December 2015