Mathematical Foundations for Finance

Question times in January
09/01, 12/01, 16/01, 19/01,
13:00 to 14:30 pm
in HG G 32.6

Course description

This course gives a first introduction to the main ideas and tools from mathematical finance. It aims at a double audience: mathematicians who want to learn the modelling ideas and concepts for finance, and non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.

Topics

• Financial market models in finite discrete time
• Absence of arbitrage and martingale measures
• Valuation and hedging in complete markets
• Basic facts about Brownian motion
• Stochastic integration
• stochastic calculus: Ito's formula, Girsanov transformation, Ito's representation theorem
• Black-Scholes formula

Prerequisites

• Results and facts from probability theory as in the book "Probability Essentials" by J. Jacod and P. Protter will be used freely.
• Especially participants without a direct mathematics background are strongly advised to look at the exercises in Chapters 8, 9, 22-25, 28 of the Jacod/Protter book. If these pose problems, you will have a hard time during the course. So be prepared.

Lecture notes

• Lecture notes will be sold in the first lecture and exercise class as well as during the question times ("Präsenz") (Price: 20 CHF).

Exercise classes

• Details of the exercise classes can be found here.

Question times ("Präsenz") and office hour

• There are regular question times ("Präsenz") on Mondays and Thursdays, 12:00 to 13:00 in HG G 32.6.
• Students who cannot come to the regular questions times (e.g. because they have to work then) are invited to come to the office hour on Fridays, 8:15 to 9:00 in HG J 44.
  

Examination details

• A NUMERICAL GRADE and ETCS points for the course are based only on the written final exam.
• Only students who get the so-called ''Testat'' are admitted to the final exam.
  
• Only students who solve at least 2/3 of all exercise sheets get the "Testat".

Written exam

• Date: 28/01/2012
  
• Time: 09:00 - 12:00
  
• Room: HIL G 61
  
• Length: 180 min
  
• No aiding materials allowed

References

• "Probability Essentials", J. Jacod and P. Protter , Springer, 2003.
• "Introduction to Stochastic Calculus Applied to Finance", D. Lamberton, B. Lapeyre, Chapman-Hall, 2008.
• "Stochastic Finance: An Introduction in Discrete Time", H. Föllmer, A. Schied, de Gruyter, 2011.