This course is concerned with the mathematical foundations and applications of continuous-time arbitrage pricing theory for multiple securities.
In the first part of the course, we shall prove the two fundamental theorems of asset pricing:
(a) the equivalence, modulo integrability conditions, of (1) absence of arbitrage on a market with multiple securities, (2) existence of an equivalent martingale measure, (3) existence of a state-price deflator; (b) the equivalence of (1) market completeness and (2) full rank, almost surely, of the volatility matrix.
In the second part, we will study - as much as time permits - examples for applications: (a) a general pricing formula for European vanilla options, (b) option pricing in affine models, (c) or a simplistic analysis for default timing.
The third part of this lecture is devoted to the equilibrium foundations of continuous-time finance. In particular, we will sketch an existence proof for a security-spot market equilibrium under the assumption of dynamic spanning.
Students should have some basic acquaintance with stochastic calculus (in particular, Itô's lemma and Girsanov's theorem).
T. Björk [2004]: Arbitrage theory in continuous time, 2nd
ed., Oxford: Oxford University Press.
D. Duffie [2001]: Dynamic asset pricing theory, 3rd ed.,
Princeton (NJ): Princeton University Press.
B. Øksendal [2007]: Stochastic differential equations. An
introduction with applications, 6th ed., Berlin: Springer.
J.M. Steele [2001]: Stochastic calculus and financial applications, New York: Springer.
The main reference for this course will be Duffie [2001].
Rhythmus | Tag | Uhrzeit | Format / Ort | Zeitraum |
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Studiengang/-angebot | Gültigkeit | Variante | Untergliederung | Status | Sem. | LP | |
---|---|---|---|---|---|---|---|
Betriebswirtschaftslehre / Diplom | (Einschreibung bis SoSe 2005) | B5; WP06; WP09; WP15 | 4 | HS | |||
Economic Behavior and Interaction Models / Promotion | |||||||
Economics and Management (BiGSEM) / Promotion | |||||||
Mathematik / Diplom | (Einschreibung bis SoSe 2008) | 5. 6. 7. 8. | HS | ||||
Mathematik / Master | (Einschreibung bis SoSe 2011) | 3 | |||||
QEM - Models and Methods of Quantitative Economics / Master | |||||||
Volkswirtschaftslehre / Diplom | (Einschreibung bis SoSe 2005) | V5; WP06; WP09; WP15 | 4 | HS | |||
Wirtschaftsmathematik / Diplom | (Einschreibung bis SoSe 2005) | 4 | HS | ||||
Wirtschaftsmathematik / Master | (Einschreibung bis SoSe 2011) | 4 | |||||
Wirtschaftswissenschaften / Master | (Einschreibung bis SoSe 2012) | Modul 5; Modul 12; Modul 16 | 4 | ||||
Wirtschaftswissenschaften / Master | (Einschreibung bis SoSe 2012) |