Stochastic Calculus and Finance
- Typ: Vorlesung
- Zielgruppe: Master
- Semester: WS 2017/18
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Ort:
Geb. 10.50, R. 604
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Zeit:
Blockveranstaltung
Termine siehe Ilias - Beginn: 26.10.2017, siehe auch Ilias
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Dozent:
Safarian
- SWS: 2
- LVNr.: 2521331
Termine:
Do, 26./Fr, 27.10.2017, jew. 9:15 - 14:45 Uhr
Do, 09./Fr. 10.11.2017, jew. 9:15 - 14:45 Uhr
Do, 23./Fr, 24.11.2017, jew. 9:15 - 14:45 Uhr
Do, 14./Fr. 15.12.2017, jew. 9:15 - 14:45 Uhr
Do, 18./Fr, 19.01.2018, jew. 9:15 - 14:45 Uhr
Achtung, o. g. Termin ist gestrichen.
Neuer Termin:
Mi, 24.01.18, Geb. 09.21, R. 209 (Blücherstr. 17)
Do, 25.01.2018, Geb. 10.50, R. 604
Do, 08./Fr, 09.02.2018, jew. 9:15 - 14:45 Uhr
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, 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.
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