Stochastic Calculus and Finance

Wird noch bekannt gegeben.

Blockseminar, Zeiten werden noch bekannt gegeben.

Dr. Safarian

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 tempered stable processes. 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), Option pricing with tempered stable and  Levy-Processes and volatility clustering,  Optimal Portfolio and Consumption  Choice (Stochastic Control and Merton continuous time optimization  problem), Equilibrium models, Consumption-Based CAPM, Numerical Methods.

1. Dynamic Asset Pricing Theory, Third Edition by Darrell Duffie, Princeton University Press, 1996
2. Stochastic Calculus for Finance II: Continuous-Time Models by Steven E. Shreve, Springer, 2003
3. An Introduction to Stochastic Integration (Probability and its Applications) by Kai L. Chung , Ruth J. Williams, Birkhäuser,
4. Methods of Mathematical Finance by Ioannis Karatzas, Steven E. Shreve, Springer, 1998
5. Kim, Y.S.; Rache, S. T.; Bianchi, M-L; Fabozzi, F.: Financial Market Models with Levy Processes and Time-Varying Volatility, Journal of Banking and Finance, 32/7, 1363-1378, 2008