Stochastic Calculus and Finance
- Typ: Vorlesung
- Lehrstuhl: Lehrstuhl für Ökonometrie und Statistik
- Semester: WS 2015/ 2016
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Ort:
Blockveranstaltung
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Zeit:
Blockveranstaltung (siehe Termine)
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Dozent:
Safarian
- SWS: 2
- ECTS: 4.5
- LVNr.: 2521331
Stochastic Calculus and Finance
Inhalt
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 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.
Literatur
- 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
Termine
Die Blockveranstaltung wird an den folgenden Terminen stattfinden:
- Donnerstag, 12.11.2015, 9:00 – 17:00 Uhr, Geb. 20.13, Raum 006
Freitag, 13.11.2015, 9:00 – 17:00, Geb. 20.14, Raum 103.1 - Entweder: Mittwoch, 25.11.2015, 09:00 – 17:00 Uhr, Geb. 05.20, Raum 1C.01
Donnerstag, 26.11.2015, 09:00 – 17:00 Uhr, Geb. 20.13, Raum 006
Oder: Donnerstag, 26.11.2015, 09:00 – 17:00 Uhr, Geb. 20.13, Raum 006
Freitag, 27.11.2015, 09:00 – 17:00 Uhr, Geb. 20.14, Raum 103.1 - Donnerstag, 10.12.2015, 9:00 – 17:00 Uhr, Geb. 20.13, Raum 006
Freitag, 11.12.2015, 9:00 – 17:00, Geb. 20.14, Raum 103.1 - Donnerstag, 28.01.2016, 9:00 – 17:00 Uhr, Geb. 20.13, Raum 006
Freitag, 29.01.2016, 9:00 – 17:00, Geb. 20.14, Raum 103.1 - Donnerstag, 11.02.2016, 9:00 - 17:00 Uhr, Geb. 20.13, 006
Freitag, den 12.02.2016, 9:00 - 17:0 Uhr, Geb. 20.14, 103.1