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Convex Stochastic optimization

Prof. Dr. Ari-Pekka Perkkiö


Schedule and Venue

Lectures

Prof. Dr. Ari-Pekka Perkkiö

Wed 14-16

First Lecture: 17.10.2018

B045


Exercises

Prof. Dr. Ari-Pekka Perkkiö

Fri 12-14


B252

Repetitorium

Prof. Dr. Ari-Pekka Perkkiö

Fri 14-16


B039

Final Exam

Tue 10-12, 12.2.2019

B252

Retake Exam

On Request

 


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Course Description

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

The seminar Approximate Dynamic Programming covers related numerical aspects of stochastic optimization and is a suggested complement to the course.


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.

  • Exercise session 1 (26.10.2018): Exercises 3.0.1-3.1.1. in the lectures notes.
  • Exercise session 2 (2.11.2018): Thm 3.5, Thm 4.1, Ex 4.0.1, Thm 4.2 in the lectures notes.
  • Exercise session 3 (9.11.2018): Lem 4.4(1), Thm 4.5(1), Ex 4.2.1, Thm 4.8 in the lectures notes.
  • Exercise session 4 (16.11.2018): Exercises 4.2.2-4.3.2 (5 in total)  in the lectures notes.
  • Exercise session 5 (23.11.2018): Thm 4.11, 5.1 and 6.2 in the lectures notes.
  • Exercise session 6 (30.11.2018): Ex 6.1.1, 6.1.2. and Thm 6.9 in the lectures notes.
  • Exercise session 7 (7.12.2018): Cor 7.4 and Exercise 7.0.1 in the lectures notes.
  • Exercise session 8 (14.12.2018): Ex 7.0.2, Ex 7.0.3 and Lemma 8.1 in the lectures notes.
  • Exercise session 9 (21.12.2018): Ex 7.0.2, Ex 7.0.3 and Lemma 8.1 in the lectures notes.
  • Exercise session 10 (11.1.2019): Thm 4.12, 4.13, Ex 4.3.4, Thm 5.2 and Ex 5.0.2 in the lectures notes.
  • Exercise session 11 (18.1.2019): Lem 8.9,  Ex, 8.1.1,  Lem 8.12 and Thm 8.13 in the lectures notes.
  • Exercise session 12 (25.1.2019): Lem 8.14, Ex, 8.3.1, Thm 8.15 and Ex 8.3.2 in the lectures notes.
  • Exercise session 13 (25.1.2019): Ex 9.0.3, Ex, 9.1.1-9.1.2 in the lectures notes.

Final Exam

The final exam is a 120 minutes written exam.

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