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: 

1. 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.
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.

Literaturhinweise

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
6. 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