Inhalt

The course will provide rigorous yet focused training in stochastic calculus and mathematical finance. Topics to be covered:

1. Stochastic Calculus: Stochastic Processes, Brownian Motion and Martingales, Stopping Times, Local martingales, Doob-Meyer Decomposition, Quadratic Variation, Stochastic Integration, Ito Formula, Girsanov Theorem, Jump-diffusion Processes, Stable and Levy processes.
2. Mathematical Finance: Pricing Models, The Black-Scholes Model, State prices and Equivalent Martingale Measure, Complete Markets and Redundant Security Prices, Arbitrage Pricing with Dividends, Term-Structure Models (One Factor Models, Cox-Ingersoll-Ross Model, Affine Models), Term-Structure Derivatives and Hedging, Mortgage-Backed Securities, Derivative Assets (Forward Prices, Future Contracts, American Options, Look-back Options), Incomplete Markets, Markets with Transaction Costs, Optimal Portfolio and Consumption  Choice (Stochastic Control and Merton continuous time optimization  problem, CAPM), Equilibrium models, Numerical Methods.

Literatur

1. Dynamic Asset Pricing Theory, Third Edition by D. Duffie, Princeton University Press, 1996
2. Stochastic Calculus for Finance II: Continuous-Time Models by S. E. Shreve, Springer, 2003
3. Stochastic Finance: An Introduction in Discrete Time by H. Föllmer, A. Schied, de Gruyter, 2011
4. Methods of Mathematical Finance by I. Karatzas, S. E. Shreve, Springer, 1998
5. Markets with Transaction Costs by Yu. Kabanov, M. Safarian, Springer, 2010