Stochastic integration 2003-2004
Contents
Stochastic calculus is an indispensable tool in modern financial mathematics.
In this course we present this mathematical theory and apply it to the problem
of pricing and hedging of financial derivatives. We treat the following topics
from martingale theory and stochastic calculus: martingales in discrete and
continuous time, construction and properties of the stochastic integral, Ito's
formula, Girsanov's theorem, stochastic differential equations. As an
application, we explain how stochastic differential equations are typically used
to model financial markets and we discuss the problem of the pricing of
derivatives such as stock options.
Literature
Brownian motions and stochastic calculus, I. Karatzas and S.E. Shreve
Continuous martingales and Brownian motion, D. Revuz and M. Yor.
Lecture notes (based on these books) will be written during the course and are available
both in pdf and in ps. Readers are kindly requested to report
errors of any kind.
Lecturer
P.J.C. Spreij
Schedule
Spring semester, Thursdays 13-16, room P.015B, first class on
February 5. No classes on April 8.
Participants
- Vincent Leijdekker
- Walter Moreno
- Enno Veerman
- David Visser
- Philip Yau
- Valeriu Trufas
- Machiel van Kleunen
- Rutger Pijls
Programme
| Week 1 |
Lecture notes: section 1
Homework: 4 exercises from section 1.3
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| Week 2 |
Lecture notes: sections 2.1, 2.2, 2.3 (until uniqueness of DM
decomposition)
Homework: choose 4 exercises from 2.2, 2.3, 2.4, 2.7, 2.8, 2.13
|
| Week 3 |
Lecture notes: section 2.3
Homework: read the proof of theorem 2.15, and select four exercises
from 2.5, 2.6, 2.9, 2.10, 2.11, 2.12
|
| Week 4 |
Lecture notes: sections 3.1, 3.2
Homework: Two exercises from 3.1, 3.2, 3.3, and two from 3.4, 3.5, 3.7
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| Week 5 |
Lecture notes: sections 4 and 5
Homework: Two exercises from 4.1 - 4.4 and one from 4.5 - 4.8
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| Week 6 |
Lecture notes: sections 6.1, 6.2
Homework: read section 6.3, three exercises from 6.3, 6.4,
6.8, 6.11, 6.12, 6.13
|
| Week 7 |
Lecture notes: sections 7.1, 7.2, 7.3
Homework: three exercises from section 7
|
| Week 8 |
Lecture notes: section 8
Homework: three exercises (out of 7 !) from section 8
|
| Week 9 |
Lecture notes: (most of) sections 9.1-9.3
Homework: read section 9.4 and make two exercises from 9.2, 9.3, 9.5, 9.6, 9.7, 9.11,
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| Week 10 |
Lecture notes:(most of) section 10.1
Homework: three exercises from 10.3, 10.4, 10.6, 10.7, 10.8
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| Week 11 |
Lecture notes: sections 10.2 and 10.3
Homework: three exercises from 10.9 + 10.10, 10.11, 10.13, 10.14
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| Week 12 |
Lecture notes: section 11
Homework: three exercises from section 11.2
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| Week 13 |
No class
|
To Korteweg-de
Vries Instituut voor Wiskunde or to the homepage
of the master's programme.
Email: spreij@science.uva.nl
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