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.

Weiterführende Literatur:

• Dynamic Asset Pricing Theory, Third Edition. by Darrell Duffie, Princeton University Press, 1996
• Stochastic Calculus for Finance II: Continuous-Time Models, by Steven E. Shreve , Springer, 2003
• An Introduction to Stochastic Integration (Probability and its Applications) by Kai L. Chung , Ruth J. Williams , Birkhaueser,
• Methods of Mathematical Finance by Ioannis Karatzas , Steven E. Shreve , Springer 1998
• 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.
• Hull, J., Options, Futures, & Other Derivatives, Prentice Hall, Sixth Edition, (2005).

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.

Stochastische Prozesse (Poisson-Prozess, Brownsche Bewegung, Martingale), Stochastisches Integral (Integral, quadratische und Kovariation, Ito-Formeln), stochastische Differentialgleichung für Preisprozesse, Handelsstrategien, Optionspreise (Feynman-Kac), risikoneutrale Bewertungen (äquivalentes Martingalmaß, Theoreme von Girsanov), Zinsstrukturmodelle.

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Aktivität & & Arbeitsaufwand \\
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\itshape Präsenzzeit & & \\
Besuch der Vorlesung & 15 x 90min & 22h 30m \\
Besuch der Übung & 15 x 45min & 11h 15m \\
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Vor- / Nachbereitung der Vorlesung & & 22h 30m \\
Vor- / Nachbereitung der Übung & & 11h 15m \\
Skript 2x wiederholen & 2 x 20h & 40h 00m \\
Klausurvorbereitung & & 40h 00m \\
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Summe & & 147h 30m \\
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\captionArbeitsaufwand für die Lerneinheit "Stochastic Calculus and Finance"