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Convex Stochastic optimization

Prof. Dr. Ari-Pekka Perkkiö


Schedule and Venue

Lectures

Prof. Dr. Ari-Pekka Perkkiö

Wed 12-14

First Lecture: 16.10.2019

B252


Exercises

Prof. Dr. Ari-Pekka Perkkiö

Tue 10-12

First Exercises: 24.10.2019

QuantLab B121


Final Exam

Wed 12-14

19.2.2020

 QuantLab B121

Retake Exam

On Request

 


News

  • The lecture notes of the previous winter semester are available online, but the notes will be completely revised.

Course Description

Introduction to convex stochastic optimization with focus on financial mathematics: convexity, normal integrands, the dynamic programming principle, Markovian dynamics, convex conjugates, dual problems, optimality conditions, stochastic control, optimal investment, illiquidity, indifference pricing.


References

  • R.T. Rockafellar, Conjugate duality and Optimization, SIAM, 1974.
  • R.T. Rockafellar and R.J-B. Wets, Variational analysis, Springer-Verlag, 2004

For whom is this course?

Target Participants: Bachelor students of Business Mathematics and master students of Financial and Insurance mathematics.

Pre-requisites: Probability Theory.

Applicable credits:

The course can be recognized as "Themen der Wirtschaftsmathematik und verwandter Gebiete I (WP9)" (6 ECTS) for bachelor students, and as "Fortgeschrittene Themen aus der Finanzmathematik B (WP61)" (6 ECTS) for master students.

 


Exercises and lectures notes

The lecture notes and exercises are uploaded here on a weekly basis.

Theoretical exercises are to be made before the exercise session. Please be prepared to present your solutions during the class.

  1. (Exercise session 24.10.): Exercises 3.0.1-3.0.5. in the lectures notes.
  2. (Exercise session 5.11.): Thm 3.5, Ex. 4.0.1., Thm 4.1, Ex 4.0.2, Ex 4.0.4.
  3. (Exercise session 12.11.): Thm 4.4, Ex. 4.1.1., Thm 4.6, Thm 4.7, Ex 4.1.2.
  4. (Exercise session 19.11.): Thm 4.10, Lem 4.12, Thm 4.13, Cor 5.2, Thm 5.7.
  5. (Exercise session 26.11.): Ex 5.0.1, Lem 6.3, Ex 6.0.1, Ex 6.0.2 (2 points).
  6. (Exercise session 3.12.): Computer exercises (assignments handed out in the class).
  7. (Exercise session 10.12.): Computer exercises (assignments handed out in the class).
  8. (Exercise session 17.12.): Lem 6.7, Ex 7.1.1 (2 points), Thm 7.14 (2 points).
  9. (Exercise session 7.1.): Ex 7.4.1-7.4.5.
  10. (Exercise session 14.1.): Ex 8.0.1, Thm 8.3, Ex 8.1.2-8.1.4.
  11. (Exercise session 21.1.): Ex 8.1.5-8.1.6, Thm 8.6-8.8.
  12. (Exercise session 28.1.): Thm 8.10, Ex 8.2.1, Thm 8.13, Thm 8.17 (2 points).
  13. (Exercise session 3.2.): Ex 9.0.1-9.0.2, Ex 9.0.3. (3 points).

Final Exam

The final exam is a 120 minutes written exam.

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