Stochastic Analysis

• 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; 
  • Ito-formula;
  • 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.