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Präsenz/Online gemischt
Event
Stochastic Calculus and Finance [WS202521331]
Type
lecture (V)Präsenz/Online gemischt
Term
WS 20/21SWS
2Language
EnglischAppointments
0Lecturers
Organisation
- KIT-Fakultät für Wirtschaftswissenschaften
Part of
- Brick Stochastic Calculus and Finance | Industrial Engineering and Management (M.Sc.)
- Brick Stochastic Calculus and Finance | Economics Engineering (M.Sc.)
- Brick Stochastic Calculus and Finance | Information Systems (M.Sc.)
- Brick Stochastic Calculus and Finance | Information Engineering and Management (M.Sc.)
- Brick Stochastic Calculus and Finance | Economathematics (M.Sc.)
Literature
- 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
- Introduction to Stochastic Calculus Applied to Finance by D.Lamberton, B. Lapeyre, Chapman&Hall,1996
Note
Learning objectives:
After successful completion of the course students will be familiar with many common methods of pricing and portfolio models in finance. Emphasis we be put on both finance and the theory behind it.
Content:
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.
Workload:
Total workload for 4.5 CP: approx. 135 hours
Attendance: 30 hours
Preparation and follow-up: 65 hours