MAT4701 - Spring 2009

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
29.04.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? N.B. 3 hours lectures today.

Exercise session and revision

?Here is a summary of the topics treated in class.?

22.04.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? N.B. 3 hours lectures today.

Hedging of contingent claims. Method based on Backward Kolmogorov equation and their representation (Markovian setting). Method based on stochastic differentiation (non-anticipating derivative).

References: [?] Section 12.3 (second part)

Material: Note on non-anticipating derivative

Suggested exercises: [?] 12.9, 12.12, 12,16 ?

21.04.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? Pricing of contingent claims

References: [?] Section 12.3 (first part)?

15.04.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? Replicable claims, market completeness

References: [?] Section 12.2

Suggested exercises: [?] 12.2, 12.3, 12.4, 12.6, 12.7.?

14.04.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? Admissible portfolios, arbitrage opportunities, fundamental theorem, contingent claims

References: [?] Section 12.1, 12.2?

01.04.2009? ? ? No classes?
31.03.2009Asma Kheder ? Sem. rom B70, NHA's Hus? ? Exercise session?
25.03.2009GdN? Sem. rom B70, NHA's Hus? Introduction to continuous time market modelling? Market model, securities, portfolios, self-financing portfolios and the meaning of self-financing

[?] Section 12.1?

24.03.2009GdN? Sem. rom B70, NHA's Hus? Feynman-Kac formula? [?] Section 8.2.

?Here is a summary of the topics treated in class.?

18.03.2009Asma Kheder ? Sem. rom B70, NHA's Hus? ? Exercise session?
17.03.2009Asma Kheder? Sem. rom B70, NHA's Hus? ? Exercise session?
11.03.2009GdN? Sem. rom B70, NHA's Hus? Kolmogorov SDE and the representation of the solution.? Completion of the arguments in [?] Chapter 7. [?] Section 8.1.

Suggested exercises: [?] 7.4, 7.13, 7.18, 7.19, 8.1, 8.2, 8.5, 8.6

Here is a summary of the topics treated in class.?

10.03.2009GdN? Sem. rom B70, NHA's Hus? Ito diffusion? Infinitesimal generator of a diffusion, Dynkin formula characteristic operator, examples of application.

Ref. [?] Chapter 7.

?

04.03.2009GdN? Sem. rom B70, NHA's Hus? Ito diffusions? Strong Markov property, generalized strong Markov property and shift operators. Infinitesimal generator of a diffusion.

Ref. [?] Chapter 7.

Suggested exercises: [?] 7.1, 7.2, 7.3, 7.10, 7.11.?

03.03.2009GdN? Sem. rom B70, NHA's Hus? Ito diffusions? Time-homogenuity, Markov property.

Ref. [?] Chapter 7.?

25.02.2009GdN? Sem. rom B70, NHA's Hus? Girsanov theorem and weak solutionf of an SDE? Corollaries of the Girsanov theorem and their use in the study of weak solutions to SDEs. Discussion on the Girsanov theorem and extensions of measures at infinity.

Ref. [?] Section 8.6 and Exercise 8.11. [KS] Section 3.5 and 5.3.B.

Suggested exercises: [?] 8.12, 8.13.

?Here is a summary of the topics treated in class.?

24.02.2009GdN ? Sem. rom B70, NHA's Hus? Girsanov theorem.? Absolutely continuous measures, Radon-Nikodym derivatives and filtrations, Girsanov theorem and Novikov condition.?
18.02.2009GdN ? Sem. rom B70, NHA's Hus? Weak solution of an SDE? Discussion in full detail of the Tanaka equation: existence of the weak solution, but not of the strong solution. Weak uniqueness but not strong uniqueness.

Here is a summary of the topics treated in class.

Here is the not on the passage between the uniqueness in the sense of modification and the uniqueness in the sense of paths. The note is written by Jan Olav Halle.?

17.02.2009GdN ? Sem. rom B70, NHA's Hus? Concept of Uniqueness of a solution. Solution to a general linear SDE? Reference for this is [KS] from page 160.

Suggested exercises: [?] 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, 5.9, 5.10, 5.11, 5.12, 5.18. ?

11.02.2009Asma Khedher? Sem. rom B70, NHA's Hus? ? Exercise session?
10.02.2009Asma Khedher? Sem. rom B70, NHA's Hus? ? Exercise session?
04.02.2009GdN ? Sem. rom B70, NHA's Hus? Introduction to SDE? Existence and uniqueness of a strong solution for an SDE.?
03.02.2009GdN ? Sem. rom B70, NHA's Hus? Ito formula ? Completion of [?] Chapter 4 and Exercise session. In particular, Ito formula 1-dimensional and d-dimensional. Tanaka formula (see [?] Exercise 4.10).

Suggested exercises: [?] 4.1, 4.2, 4.3, 4.4, 4.6, 4.7, 4.11, 4.12, 4.13, 4.14, 4.16?

28.01.2009GdN ? Sem. rom B70, NHA's Hus? Local martingales, generalization of the Ito integral? Here is a summary of the topics treated in class.

A set of suggested exercises is here and here

Moreover you can try: [?] 4.5, 7.8, 7.12?

27.01.2009GdN ? Sem. rom B70, NHA's Hus? The Ito representation theorem, martingale representation theorem, stopping times? Here is a summary of the topics treated in class.?
21.01.2009GdN? Sem. rom B70, NHA's Hus? Ito stochastic calculus? Here is a summary of the topics treated in class.?
20.01.2009GdN? Sem. rom B70, NHA's Hus? Regularity of the paths of Brownian motion, p-variations, predictability? ?
14.01.2009GdN? Sem. rom B70, NHA's Hus? Revision of elements of the theory of stochastic processes and Brownian motion? Here is a summary of the topics treated in class.

A set of suggested exercises is here?

13.01.2009Giulia diNunno? Sem. rom B70, NHA's Hus? Revision of elements of measure theory and probability? Welcome to the course!

Here is a summary of the topics treated in class.

A set of suggested exercises is here?

Published Jan. 8, 2009 12:26 PM - Last modified May 11, 2009 8:57 PM
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