This course covers the fundamental principles and techniques of Financial Mathematics in discrete- and continuous-time models. 

Specific topics are

• Financial market models in discrete time: arbitrage freeness and completeness     
• Conditional expectation and discrete time martingales
• Valuation of European, American and path-dependent options
• Foundations of continuous time market models and of the Black-Scholes model
• Interest rate models and derivatives 
• Risk measures
• Portfolio optimisation and CAPM

More information is given in Moodle. Please inscribe there for the course.

A list of reference books would cover the following works:

• A. Irle, Finanzmathematik: Die Bewertung von Derivaten, Vieweg + Teubner, 2012.
• N.H.Bingham & R.Kiesel, Risk Neutral Valuation, 2nd ed., Springer, 2004.
• H. Föllmer & A. Schied, Stochastic Finance: An introduction in discrete time, de Gruyter, 2004.
• P.K. Koch & S. Merino, Mathematical Finance and Probability: A Discrete Introduction, Springer, 2013.
• M. Musiela & M. Rutkowski, Martingale methods in financial modelling, 2nd ed., Springer, 2004.
• S. Shreve, Stochastic Calculus for Finance I: The  Binomial Asset Pricing Model, Springer, 2004.
• S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004.