The course will provide rigorous yet focused training in stochastic calculus and mathematical finance. Topics to be covered:
- 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.
- 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.
- Dynamic Asset Pricing Theory, Third Edition by Darrell Duffie, Princeton University Press, 1996
- Stochastic Calculus for Finance II: Continuous-Time Models by Steven E. Shreve, Springer, 2003
- An Introduction to Stochastic Integration (Probability and its Applications) by Kai L. Chung , Ruth J. Williams, Birkhäuser,
- Methods of Mathematical Finance by Ioannis Karatzas, Steven E. Shreve, Springer, 1998
- 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