311506 Dynamic Financial Markets (Finance 2a) (V) (WiSe 2010/2011)

This course, given for four hours weekly during the first half of the semester, covers some basic topics of the theory of dynamic financial markets.

At the outset, the general one-period model, with a particular emphasis on the two fundamental theorems of asset pricing will be presented.

We will then move on to a discussion of stochastic integrals, Itô's formula, stochastic differential equations, infinitesimal generators (in Björk's terminology: infinitesimal operators), partial differential equations, and the Black-Scholes model.

Our presentation will follow the classical (rather than a simplified infinitesimal) approach to stochastic analysis, based on measure-theoretic probability theory and linear functional analysis.

In the second half of the semester, the lecture course will be continued as course no. 311506 Continuous-Time Finance (Finance 2b).

Requirements for participation, required level

A good working knowledge of (measure-theoretic) probability theory is essential, and some acquaintance with linear functional analysis would also be helpful.

In order to understand the economic consequences of the mathematical ideas and results presented in this lecture course, some familiarity with financial markets (e.g. Finance 1a/b) is necessary.

Bibliography

T. Björk [2004]: Arbitrage theory in continuous time, 2nd
ed., Oxford: Oxford University Press.
D. Duffie [2001]: Dynamic asset pricing theory, 3rd ed.,
Princeton (NJ): Princeton University Press.
A. Etheridge [2002]: A course in financial calculus, Cambridge: Cambridge University Press.
J.M. Steele [2001]: Stochastic calculus and financial applications, New York: Springer.

F. Herzberg [2010]: Lecture Notes on Finance 2-3, Bielefeld University