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Stochastic Calculus and Finance

Stochastic Calculus and Finance
Typ: Vorlesung (V) Links:
Zielgruppe: Master
Semester: WS 19/20
Ort:

Blockveranstaltung, Termine werden über Ilias bekanntgegeben

Zeit:

Blockveranstaltung, Termine werden über Ilias bekanntgegeben

Dozent: Dr. Mher Safarian
SWS: 2
LVNr.: 2521331

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, 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.

 

Literaturhinweise

Wird in der Vorlesung bekannt gegeben.

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).