MAT4711 - Spring 2008

Undervisningsplan

DatoUndervises avStedTemaKommentarer / ressurser
01.04.2008GdN? B1036 NHA's Hus? Kolmogorov equation? Welcome to the course!

This is the follow up course of MAT4700. The topics covered in that course constitute the basic knowledge to follow MAT4711.

Topic: PDEs and diffusion the connection through the generator. Representation of the solution of the Cauchy problems presented: The Feynman-Kac formula.?

02.04.2008GdN? B1036 NHA's Hus? About Kolmogorov equation. About absolutely continuous probability measures? Conclusion of the proofs related to the representation of the solution of the Cauchy problems studied. Introduction to the Girsanov change of measure.

Suggested exercises: [?] 8.1, 8.2, 8.5, 8.6. ?

04.04.2008GdN? Auditorium 3 Vilhelm Bjerknes hus ? Girsanov Theorem? Main result with proof.

Suggested exercises: [?] 8.11, 8.12 and and here?

08.04.2008GdN? B1036 NHA's Hus ? Girsanov theorem and weak solution of differential equations? Conclusion of the chapter.

Suggested exercises:[?] 8.13, 8.15.?

09.04.2008GdN? B1036 NHA's Hus ? Optimal stopping problem. Introduction. ? Study of the optimal reward in the optimal stopping problem and existence of a solution.

Suggested exercises: [?] 10.1, 10.2?

11.04.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus ? Exercise session? ?
15.04.2008? ? ? No classes?
16.04.2008GdN? B1036 NHA's Hus ? Optimal stopping problem.? Uniform integrability (short introduction). Example of optimal stopping problem. More about "uniqueness" of an optimal stopping problem. How to generalize the problem.

Suggested exercises: [?] Example 10.1.14, 10.2.1, [?] 10.3, 10.4, 10.7

Suggested exercises [?] Example 10.2.2, Exercise 10.5.

Summary of the topics covered so far are: here (about Kolmogorov backward equations)and here (about the Girsanov theorem). As for optimal stopping problem read here??

18.04.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus ? Exercise session? ?
25.04.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus ? A bit on optimal stopping problems and exercise session ? Section 10.3 and Section 10.4.

Suggested exercises: [?] Exercises 10.13, 10.14, 10.16?

29.04.2008GdN ? B1036 NHA's Hus ? Introduction to stochastic control? Stochastic control problems. Admissible controls and details on Markov controls.?
30.04.2008GdN ? B1036 NHA's Hus ? Stochastic control? HJB-equations as necessary conditions for value functions and optimal control values. Verification theorem. Markov controls versus adapted controls.?
06.05.2008? ? ? No classes?
07.05.2008ATTK ? B1036 NHA's Hus? Exercise session? ?
09.05.2008ATTK ? Auditorium 3 Vilhelm Bjerknes hus? Exercise session? ?
13.05.2008GdN? B1036 NHA's Hus? Stochastic control ? Stochastic control completion of the section. Example: an optimal selection problem

Suggested exercises: [?] Exercises 11.1, 11.7, 11.8, 11.10, 11.4, 11.12. 8.18

Summary of the topics covered so far are: here ?

14.05.2008GdN ? B1036 NHA's Hus? Applications to mathematical finance? Stock market and derivative market, introduction. Market model, strategies, self-financing strategies, admissible strategies, arbitrage opportunities. Fair market.

Suggested exercises. [?] 11.11 ?

16.05.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus? Exercise session? ?
20.05.2008GdN? B1036 NHA's Hus? Applications to mathematical finance? Arbitrage and equivalent (local) martingale measures.?
21.05.2008GdN ? B1036 NHA's Hus? Applications to mathematical finance? Contingent claims, pricing, hedging.

Summary of the topics covered in this are is: here

Suggested exercises: [?] 12.1, 12.2, 12.3, 12.5, 12.6, 12.7, 12.8, 12.9, 12.10, 12.12. And also 11.2.?

23.05.2008ATTK ? Auditorium 3 Vilhelm Bjerknes hus ? Exercise session? ?
27.05.2008GdN? B1036 NHA's Hus ? Applications to mathematical finance? Hedging and backward stochastic differential equations. Completion of the program and reading of the "pensum".

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28.05.2008ATTK? B1036 NHA's Hus ? Exercise session ? ?
30.05.2008ATTK? Auditorium 3 Vilhelm Bjerknes hus ? Exercise session ? ?
Published Jan. 3, 2008 1:15 PM - Last modified May 21, 2008 12:27 PM
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