Lecturer
Hanspeter Schmidli
Content
In the theory of stochastic processes the Markov processes are of special interest because martingales can be constructed in quite a simple way. For this purpose the so-called generator of the Markov process is used. Martingales are an important tool in Applied Probability. They lead to first passage probabilities as well as to the Feynman-Kac formula. The latter is of special interest in Mathematical Finance, because it links prices of derivatives with partial differential equations. After an introduction to semi-group theory, the martingale problem is studied.
Prerequisites
Probability 1 and Probability 2.
Literature
Chapters 1 and 4 of S.N. Ethier and T.G. Kurtz: Markov Processes, John Wiley & Sons, New York, 1986.