Mathematical Foundations for Finance

Question times in January
10/01, 13/01, 17/01, 20/01,
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 familiarise themselves with those tools either before or during the course.

Lecture notes

Lecture notes will be sold in the first lecture and during the "Präsenz" (Price: 20 CHF).

Exercise classes

Details of the exercise classes can be found here.

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 correctly get the "Testat".

Written exam

• Date: 07/02/2011
• Time: 09:00 - 11:00
  
• Room: HIL G 61
• Length: 120 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, 2004.