This class is a natural extension to Probability and Finance I taught
by Prof. Fabio Trojani to continuous random variables along with an
introduction to continuous-time stochastic processes. The focus will be
on applications that are relevant in today´s market practice as well as
academics. After having taken the course you will have good knowledge of
the models that are around and also how to work with them.
For all topics covered many examples will deepen our intuition and un- derstanding. The main textbook is Shreve (2004). We will occasionally use Bjo rk (1998), Brigo and Mercurio (2006), Øksendahl (2000) as well as original research papers.
There will be a final closed-book written exam
Topics in Detail
Some of the below topics you will already have covered in Probability and Finance I. In that case we will concentrate on the extensions necessary to accommodate our more elaborate sample spaces. I will also take the liberty to include and exclude topics as we go along.
Bjo rk, T. (1998). Arbitrage Theory in Continuous Time. Oxford University Press.
Brigo, D. and Mercurio, F. (2006). Interest Rate Models – Theory and Prac- tice. With Smile, Inflation and Credit. Springer Finance. Springer-Verlag, 2nd edition.
Øksendahl, B. (2000). Stochastic Differential Equations. Springer.
Shreve, S. E. (2004). Stochastic Calculus for Finance II, Continuous-Time Models. Springer, Berlin.