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Stochastic Calculus and Finance

Stochastic Calculus and Finance
Typ: Vorlesung
Lehrstuhl: Lehrstuhl für Ökonometrie und Statistik
Semester: WS 2014/2015
Ort:

siehe unten (unter "Hinweis/Termine")

Zeit:

(jeweils mit individuell vereinbarten Pausen!)
Do 13.11.:  9:30 - 18 Uhr
Fr 14.11.:   9:30 - 19 Uhr

Do 27.11.:  9:30 - 18 Uhr
Fr 28.11.:  11:30 - 19 Uhr

Do 11.12.:  9:30 - 18 Uhr
Fr 12,12.:   9:30 - 19 Uhr

Do 29.01:  9:30 - 19 Uhr
Fr 30.01.:  9:30 - 19 Uhr
 

Beginn: 13.11.2014
Dozent:

Safarian

SWS: 2
ECTS: 7,5
Prüfung:

Klausur

Hinweis:

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, 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

1. Dynamic Asset Pricing Theory, Third Edition by D. Duffie, Princeton University Press, 1996
2. Stochastic Calculus for Finance II: Continuous-Time Models by S. E. Shreve, Springer, 2003
3. Stochastic Finance: An Introduction in Discrete Time by H. Föllmer, A. Schied, de Gruyter, 2011
4. Methods of Mathematical Finance by I. Karatzas, S. E. Shreve, Springer, 1998
5. Markets with Transaction Costs by Yu. Kabanov, M. Safarian, Springer, 2010

Termine:

Do, 13.11.;   9:30 - 11:30 Uhr; 20.11, R. 004
                   14 - 18 Uhr; 20.13, R. 006
Fr, 14.11.;   9:30 - 19 Uhr; 20.12, R. 002

Do, 27.11.:   9:30 - 14 Uhr; 20.12, R. 002
                    14 - 18 Uhr; 20.13, R. 006
Fr, 28.11.:    11:30 - 19 Uhr; 11.40, R. 214

Do, 11.12.:    9:30 - 12 Uhr; 20.11, R. 004
                     14 - 18 Uhr; 20.13, R. 006
Fr. 12,12.:     9:30 - 19 Uhr; 20.12, R. 002

Do, 29.01:    9:30 - 19 Uhr; 20.12, R. 002
Fr, 30.01.:    9:30 - 19 Uhr; 20.12, R. 002
(bzw. mit individuell vereinbarten Pausen)

Für weitere Informationen:

Lectures

Slides