Beschreibung
The course will provide rigorous yet focused training in stochastic calculus and finance. The program will cover modern approaches in stochastic calculus and mathematical finance. Topics to be covered:
- Stochastic Calculus: Stochastic Processes, Brownian Motion and Martingales, Entropy, Stopping Times, Local martingales, Doob-Meyer Decomposition, Quadratic Variation, Stochastic Integration, Ito Formula, Girsanov Theorem, Jump-diffusion Processes, Stable and 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), Incomplete Markets, Markets with Transaction Costs, Optimal Portfolio and Consumption Choice (Stochastic Control and Merton continuous time optimization problem, CAPM), Equilibrium models, Numerical Methods.
Literaturhinweise
- Dynamic Asset Pricing Theory, Third Edition by D. Duffie, Princeton University Press, 1996
- Stochastic Calculus for Finance II: Continuous-Time Models by S. E. Shreve, Springer, 2003
- Stochastic Finance: An Introduction in Discrete Time by H. Föllmer, A. Schied, de Gruyter, 2011
- Methods of Mathematical Finance by I. Karatzas, S. E. Shreve, Springer, 1998
- Markets with Transaction Costs by Yu. Kabanov, M. Safarian, Springer, 2010
- Introduction to Stochastic Calculus Applied to Finance by D.Lamberton, B. Lapeyre, Chapman&Hall,1996
Termine und Räume
Do, 07.11.2019 Einführung
12:00 - 16:00 Uhr, Geb. 09.21, R. 209 (Blücherstr. 17)
Fr, 08.11.2019 09:00 - 13:00 Uhr Geb. 20.30 SR 0.019
Fr, 08.11.2019 13:15 - 16:00 Uhr Geb. 01.93, Raum K1
Do, 21.11.2019 9:00 - 19:00 Uhr, Geb. 01.93, R. K1
Fr, 22.11.2019 9:00 - 16:00 Uhr, Geb. 05.20, 1C-01
Do, 28.11.2019 11:30 - 19:00 Uhr, Geb. 10.50, Raum 604
Fr, 29.11.2019 09:30 - 17:00 Uhr, Geb. 01.93, Raum K1
Do, 12.12.2019 9:00 - 19:00 Uhr, Geb. 01.93, R. K1
Fr, 13.12.2019 12:30 - 16:00 Uhr, Geb. 01.93, R. K1
Do, 23.01.2020 9:00 - 19:00 Uhr, Geb. 10.50, Raum 604
Fr, 24.01.2020 9:00 - 16:00 Uhr, Geb. 01.93, R. K1
Do, 13.02.2020 9:00 - 19:00 Uhr, Geb. 01.93, R. K1
Fr, 14.02.2020 9:00 - 16:00 Uhr, Geb. 01.93, R. K1