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Convex Stochastic optimization

Prof. Dr. Ari-Pekka Perkkiö


Schedule and Venue

Lectures (4 hours)

Ari-Pekka Perkkiö

Mon 12-14

Wed 14-16

First Lecture: Wed 4.11.2020

Zoom


Exercises (2 hours)

Ari-Pekka Perkkiö

Wed 16-18

First Exercises: Wed 11.11.2020

Zoom


Final Exam

TBA

 TBA

Retake Exam

On Request

 


News

  • To register to the course, please send a email to the lecturer, perkkioe@math.lmu.de.
  • Whenever sending emails concerning with course, start the subject field with CSO2020.
  • The lecture notes of the previous winter semester are already available online, but the notes will be completely revised.
  • The course will be held online in Zoom.

Course Description

Introduction to convex stochastic optimization with focus on stochastic control and financial mathematics: convexity, normal integrands, the dynamic programming principle, Markovian dynamics, cost-to-go functions, convex conjugates, dual problems, optimality conditions, stochastic control, portfolio optimization, illiquidity, indifference pricing.


References

The course is based on a book manuscript "Convex Stochastic Optimization", which is will available in a lecture note format during the course.

  • 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: Master students of Financial and Insurance mathematics, Master students in mathematics and Bachelor students of Business Mathematics.

Pre-requisites: Probability Theory.

Applicable credits:

The course can be recognized  (9 ECTS).

 


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. All the exercises can be found in the lecture notes. Please be prepared to present your solutions during the class.

  • Exercise session 1 (11.11.2020): Theorem 8.1, Exercise 8.4.1, Theorem 8.8 and Exercise 8.4.2.
  • Exercise session 2 (18.11.2020): Lemma 8.9, Theorem 8.10, Exercise 8.4.4 and Theorem 8.1.
  • Exercise session 3 (25.11.2020): Thm 8.11, Ex 8.5.1, Thm 8.14 and Thm 8.16.
  • Exercise session 4 (2.12.2020): Ex 8.5.2, Lem 8.20 (8.20.1), Thm 8.21 (8.21.1), Thm 3.9.
  • Exercise session 5 (9.12.2020): Thm 8.24, Ex 8.7.2, Ex 8.7.3, Ex 8.7.4.
  • Exercise session 6 (16.12.2020): Ex 4.0.1, Rem 4.3, Lem 4.4 (double points).
  • Exercise session 7 (13.1.2021): Ex 4.1.2, Rem Ex 4.1.3, Example 4.47.
  • Exercise session 8 (20.1.2021): Ex 4.52, Ex 4.52, Ex. 4.3.1, Ex. 4.3.2.
  • Exercise session 9 (20.1.2021): Ex 8.8.1, Ex. 8.8.2, Ex 8.8.3, Thm 8.27, Thm 8.28.
  • Exercise session 10 (3.2.2021): Ex 8.9.1, Ex 7.1.2., Example 6.8.

Final Exam

The final exam is a 120 minutes written exam.

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