Stochastic Finance II

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.