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Stochastic Calculus and Finance

Stochastic Calculus and Finance
Typ: Vorlesung
Lehrstuhl: Statistik, Ökonometrie und Mathematische Finanzwirtschaft
Semester: WS 2012/2013

Geb. 20.13, 006 (V)
Geb. 20.13, 006 (Ü)


Freitag, 09:45 – 11:15 (V)
Freitag, 11:30 – 13:00 (Ü)

Beginn: 19.10.2012


SWS: 4
LVNr.: 2521331
Prüfung: Mündlich, nach Vereinbarung

To be held in English

The course will provide rigorous yet focused training in stochastic calculus and mathematical finance. Topics to be covered:
1. 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.
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), 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.

1. Dynamic Asset Pricing Theory, Third Edition by Darrell Duffie, Princeton University Press, 1996
2. Stochastic Calculus for Finance II: Continuous-Time Models by Steven E. Shreve, Springer, 2003
3. An Introduction to Stochastic Integration (Probability and its Applications) by Kai L. Chung , Ruth J. Williams, Birkhäuser,
4. Methods of Mathematical Finance by Ioannis Karatzas, Steven E. Shreve, Springer, 1998
5. Kim Y.S. ,Rachev 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.