- This course provides a general detailed introduction into the stochastic integration theory for continuous semi-martingales (a class of stochastic processes encompassing Brownian motion) and stochastic differential equations. The concepts taught are highly relevant for many areas of statistics, (numerical) analysis as well as financial and insurance mathematics. Stochastic analysis is also the basis for many models in the natural and social sciences or engineering.
- Wiener process;
- Martingale theory;
- Stochastic integration for continuous semi-martingales;
- Stochastic Exponential;
- Stochastic differential equations;
Lecture Notes and Exercises
All materials will be available on Moodle.
- Bingham, N. H. and Kiesel, R.: Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives. (Springer) 2nd edn., 2004.
- Karatzas, I. and Shreve, S.: Brownian Motion and Stochastic Calculus. (Springer), 1998.
- Lamberton, D. and Lapeyre, B.: Introduction to stochastic calculus applied to finance. (Chapman & Hall), 2nd edn., 2008.
- Oksendal, B.: Stochastic Differential Equations. (Springer, Berlin), 5th edn., 1998.
- Shiryaev, A.: Essentials of Stochastic Finance. (World Scientifc), 1999.
- Revuz, D. and Yor, M.: Continuous Martingales and Brownian motion. (Springer), 1999.
- Shreve, S.: Stochastic Calculus for Finance II: Continuous-Time Model. (Springer), 2004.
- Steele, M.: Stochastic Calculus with Financial Applications. (Springer), 2001.
You can also find the literature in the Semesterapparat.
Time and Venue
- The institute is offering all courses originally planned starting April 20th. Teaching will take place online using the university's moodle system. Further information is available on the moodle system.
- The course will be taught in the first half of the summer term 2020. It is a (2+1)-course and there will be 4 hours of lecture and 2 hours of exercise every week. Immediately after the course students may attend the following course Financial Mathematics II, which applies results from the course to financial mathematics in continuous time.
- Master Mathematik (optional)
- Master Wirtschaftsmathematik (optional)
- Master Mathematische Biometrie (optional)
- Master of Finance-Major Financial Mathematics (obligatory)
- Master of Finance-Major Financial Economics (optional)
- Master of Finance-Major Actuarial Science (optional)
- Elementary Probability and Measure Theory or Introduction to Measure Theoretic Probability
- Recommended: Stochastics II