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Stochastic Calculus and Finance

Stochastic Calculus and Finance
Typ: Vorlesung
Lehrstuhl: Lehrstuhl für Ökonometrie und Statistik
Ort:

Block 1:
Do, 14.11., 9:45 - 13:00 Uhr:
Geb. 20.13, Raum 001
Do, 14.11., 14:00 - 19:00 Uhr:
Geb. 20.13, Raum 006
Fr,15.11., 9:45 - 19:00 Uhr,
Geb. 20.11, Raum 004
(= Promotionsraum, rechts ganz hinten)

Block 2:
28. und 29.11.2013,
jeweils 9:45 - 19:00 Uhr
Geb. 20.11, Raum 004 (Promotionsraum)

Block 3:
13.12.13, 9:45 - 13:00 Uhr:
Geb. 20.13, Raum 001
13.12.13, 14:00 - 19:00 Uhr:
Geb. 20.20 (RZ), Raum 171.1
14.12.13, 9:45 - 19:00 Uhr:
Geb. 20.13, Raum 001

Block 4:
30. und 31.01.2014,
jeweils 9:45 - 19:00 Uhr
Geb. 20.12, Raum 002

Zeit:

Blockseminar, Räume und Zeiten der nächsten Blöcke werden an dieser Stelle in Kürze bekanntgegeben.

Beginn: 14.11.2013
Dozent:

Dr. Safarian

SWS: 2
LVNr.: 2521331
Hinweis:

Inhalt

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 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), 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