MAT4701 - Spring 2009

Undervisningsplan

Dato Undervises av Sted Tema Kommentarer / ressurser
29.04.2009 GdN  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. 
22.04.2009 GdN  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  
21.04.2009 GdN  Sem. rom B70, NHA's Hus  Introduction to continuous time market modelling  Pricing of contingent claims

References: [?] Section 12.3 (first part) 
15.04.2009 GdN  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. 
14.04.2009 GdN  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 
31.03.2009 Asma Kheder   Sem. rom B70, NHA's Hus    Exercise session 
25.03.2009 GdN  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 
24.03.2009 GdN  Sem. rom B70, NHA's Hus  Feynman-Kac formula  [?] Section 8.2.

 Here is a summary of the topics treated in class. 
18.03.2009 Asma Kheder   Sem. rom B70, NHA's Hus    Exercise session 
17.03.2009 Asma Kheder  Sem. rom B70, NHA's Hus    Exercise session 
11.03.2009 GdN  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. 
10.03.2009 GdN  Sem. rom B70, NHA's Hus  Ito diffusion  Infinitesimal generator of a diffusion, Dynkin formula characteristic operator, examples of application.

Ref. [?] Chapter 7.

 
04.03.2009 GdN  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. 
03.03.2009 GdN  Sem. rom B70, NHA's Hus  Ito diffusions  Time-homogenuity, Markov property.

Ref. [?] Chapter 7. 
25.02.2009 GdN  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. 
24.02.2009 GdN   Sem. rom B70, NHA's Hus  Girsanov theorem.  Absolutely continuous measures, Radon-Nikodym derivatives and filtrations, Girsanov theorem and Novikov condition. 
18.02.2009 GdN   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. 
17.02.2009 GdN   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.  
11.02.2009 Asma Khedher  Sem. rom B70, NHA's Hus    Exercise session 
10.02.2009 Asma Khedher  Sem. rom B70, NHA's Hus    Exercise session 
04.02.2009 GdN   Sem. rom B70, NHA's Hus  Introduction to SDE  Existence and uniqueness of a strong solution for an SDE. 
03.02.2009 GdN   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 
28.01.2009 GdN   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 
27.01.2009 GdN   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. 
21.01.2009 GdN  Sem. rom B70, NHA's Hus  Ito stochastic calculus  Here is a summary of the topics treated in class. 
20.01.2009 GdN  Sem. rom B70, NHA's Hus  Regularity of the paths of Brownian motion, p-variations, predictability   
14.01.2009 GdN  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 
13.01.2009 Giulia 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 Dec. 9, 2024 1:50 PM
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