Partial Differential Equations with Applications in Finance VT22
General Information
The general information can be found here. Zoom room for the first lecture:
- Meeting ID: 653 6853 0180
- Passcode: 314159
The lecture notes, recommended readings, exercises, solutions, etc., if exist, will be found below. Video recordings and past exams available upon request. If you have any questions, you can
- Email me (yuqiong.wang@math.uu.se)
- Schedule a visit at Å14209
Lecture notes
| Lecture | Recommended reading | Lecture notes |
|---|---|---|
| Lecture 1 | Oksendal p7-11 (probability) p12-14 (Brownian motion), Appendix B (Conditional expectation) | F1.pdf |
| Lecture 2 | Oksendal p26-30 (construction of Ito integrals), p70-74 (proof of the existence and uniqueness of the strong solution), A useful inequality: Grönwall's inequality (also see Oksendal exercise 5.17) | F2.pdf |
| Lecture 3 | Oksendal §4.1-4.2 (Ito's formula) | F3.pdf |
| Lecture 4 | Oksendal §7.3, a recap on Black Scholes PDE see Lalley. Wald's identities for Brownian motion | F4.pdf |
| Lecture 5 | Page 1 to 8 of Kohn section 1 | F5.pdf |
| Lecture 6 | Heat equation related see §2.3 of Lawrence C. Evans, more related material see next lecture. | F6.pdf |
| Lecture 7 | Kohn section 2 page 7-9. | F7.pdf |
| Lecture 8 | Kohn section 1 page 10-15 (the stationary distribution paragraph on page 12 is not very rigorous, see the lecture notes for derivation). | F8.pdf |
| Lecture 9 | The best reference for this module is Bjork. (I'm using 3rd ed here. Apparently there is a 4th ed. Check §25 there, but be careful of the notations). | F9.pdf |
| Lecture 10 | Bjork chapter 19. | F10.pdf |
| Lecture 11 | Kohn section 6 P1-P6. | F11.pdf |
| Lecture 12 | Kohn section 6 P6-P9. | F12.pdf |
List of exercises and sketch of solutions
| Lesson | Exercises | Sketch of solutions |
|---|---|---|
| List I | List of exercises I.pdf | Upon request |
| List II | List of exercises II.pdf | Upon request |
| List III | List of exercises III.pdf | Upon request |
Hand-in assignments and sketch of solutions
| Assignment | Sketch of solutions |
|---|---|
| Assignment_1.pdf | Sol_upp1.pdf |
| Assignment_2.pdf | Sol_upp2.pdf |