Webrelaunch 2020

Continuous Time Finance (Sommersemester 2024)

Vorlesung: Dienstag 9:45-11:15 20.30 0.019
Mittwoch 8:00-9:30 20.30 0.014
Übung: Donnerstag 14:00-15:30 20.30 -1.012
Dozentin, Übungsleiterin Prof. Dr. Vicky Fasen-Hartmann
Sprechstunde: Nach Vereinbarung.
Zimmer 2.053 Kollegiengebäude Mathematik (20.30)
Email: vicky.fasen@kit.edu
Übungsleiterin Dr. Tamara Göll
Sprechstunde: Nach Vereinbarung
Zimmer 2.014 Kollegiengebäude Mathematik (20.30)
Email: tamara.goell@kit.edu


The lecture deals with various central topics of financial mathematics in continuous time.

The contents of the lecture are split into two parts. The first part consists of an introduction to stochastic analysis. First, Brownian motion, the central stochastic process of the lecture, is introduced and important results from martingale theory are discussed. Afterwards, we derive the stochastic integral, show different properties and present its central importance in financial mathematics.

In the second part of the lecture, the focus will be on analyzing the Black-Scholes financial market. Here the stock price is modelled by a geometric Brownian motion. We will price and hedge options in such a market. The fundamental theorems of asset pricing for the Black-Scholes market are formulated, establishing relationships between the absence of arbitrage, equivalent martingale measures and completeness. Finally, portfolio optimization and interest rate structure models are discussed.

Further information

Further information can be found in Ilias.