MAT9740 - Spring 2010

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
04.03.2010GdN? Sem. rom B70 Niels Henrik Abels hus? ? ?
01.03.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Clark-Ocone formulas? [DOP] Sections 4.1, 4.2, 4.3; 12.4, 12.5, 12.6?
25.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Malliavin derivative and Skorohod integral? Continuation.

[DOP] Chapter 3 is completed. Chapter 12, Sections 12.1, 12.2, 12.3. Chapter 12 has been treated by comparison with Chapter 3. Not all was treated in detail. The completion of the arguments is left to the participants to classes.?

22.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Malliavin derivative and Skorohod integral? Continuation

[DOP] Chapter 3, 12

We have discussed the duality of the operators: Skorohod integral, Malliavin derivative and Ito integral and non-anticipating derivative. With respect to this last topic you can read about the non-anticipating derivative in:

  • "Stochastic integral representations, stochastic derivatives and minimal variance hedging", by G. diNunno, Stochastics and Stochastics Reports, 2002, 73, 181-198.
  • "Stochastic integrals and adjoint derivatives", by G. diNunno and Yu.A. Rozanov. In Stochastic Analysis and Applications, Springer 2007.
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18.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Malliavin derivative? [DOP] Chapter 3, 12

2. Normal Inverse Gaussian (NIC) distribution (by Nam)(to be presented on 18.02)?

15.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Skorohod integral? [DOP] Chapter 2, 11

Suggested exercises: [DOP] ......?

11.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus ? Ito representation theorems and chaos expansions ? [DOP] Chapters 1, 10

4. Stable processes/distributions (by Jukka)?

08.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus ? ? Special topics:

1. Poisson process and compound Poisson process (by Elin)

2. Normal Inverse Gaussian (NIC) distribution (by Nam)(to be presented on 18.02)

3. Subordinators (by Torstein)

4. Stable processes/distributions (by Jukka)(to be presented 11.02)

5. Characteristic functions and convergence of probability measures (by Steffen) ?

04.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus ? Ito representation theorems and chaos expansions? [DOP] Sections 9.3, 9.4.

Suggested exercises: [DOP] Problems 1.4, 9.1, 9.2, 9.3. ?

01.02.2010GdN? Sem. rom B70 Niels Henrik Abels hus? Introduction to Levy processes? [DOP] Section 9.1 completed. Section 9.2 self-reading.

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28.01.2010Giulia diNunno? Sem. rom B70 Niels Henrik Abels hus? Introduction to Levy processes? Welcome to the course!

Levy processes and infinitely divisible distributions. Ref [DOP] Chapter 9.

To deepen the reading [Sato]: Levy processes and infinitely divisible distributions, Cambridge 1999. Chapter 1, Chapter 2 Sections 7-9. (Diagonal reading)

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Published Jan. 11, 2010 12:01 PM - Last modified Feb. 25, 2010 3:13 PM
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