This course is about continuous time models in financial mathematics.
Content:
- Introduction to stochastic calculus and stochastic differential equations
- Risk-neutral pricing and hedging in diffusion models
- Fundamental theorem of asset pricing in continuous time
- Control theory: dynamic programming principle, HJB-equation, verification theorems, viscosity solutions; application to portfolio optimization problems
Prerequisites:
- Analysis I + II
- Linear Algebra I+II
- Stochastic I+II
Recommended, but not required:
- Stochastic Analysis (possibly in parallel)
- Financial Mathematics I
Lectures:
- Wed. 11 – 13, Room 0.311 (RUD 26) - Dörte Kreher
- Thu. 11 – 13, Room 0.310 (RUD 26) - Dörte Kreher
Tutorials:
- Thu. 9 – 11, Room 1.304 (RUD 26) - Yuchen Sun
Material
- Shreve, S.E., Karatzas, I. (2014). Brownian Motion and Stochastic Calculus. Springer.
- Shreve, S. E. (2004). Stochastic Calculus for Finance II: Continuous-Time Models. Springer.
- Pham, H. (2009). Continuous-time Stochastic Control and Optimization with Financial Applications. Springer.