The Filtering Problem and Portfolio Optimization under Partial Information – Summer Term 2019

The Filtering Problem and Portfolio Optimization under Partial Information – Summer Term 2019

On this webpage you find all information on my seminar on The Filtering Problem and Portfolio Optimization under Partial Information in the summer term 2019 at TU Berlin.

News

  • The slides presented during the second preliminary meeting are now available for download below.

Background

In many fields of applications one faces the problem of filtering the true state of a system from a noisy signal. Classical examples entail

  • Speech Recognition: Filter the actual spoken words out of a noisy sound file;
  • Parameter Estimation for Financial Models: Determine the drift or volatility of an asset price by only observing the price process.

In this seminar, we first discuss this filtering problem from a theoretical point of view before studying several applications arising in mathematical finance in the context of optimal portfolio choice in models with partially observable price processes.

General Information

Due to the large number of partipants, the seminar is split into two groups. The presentations for the respective groups are scheduled for

  • Group 1: June 29 in MA 313,
  • Group 2: June 30 in MA 313.

The precise schedule of the talks has been announced by mail.

Your presentations should not exceed 45 minutes and will be followed by a short discussion of about 10-15 minutes. You may choose the presentation format (slides or blackboard) freely. Please also prepare a handout not exceeding one sheet of paper (two-sided is fine). Active participation during all talks is expected.

There will be preliminary meeting on

  • June 14 in MA 721 at 10:15h

in which we briefly discuss the presentation format, handouts, and grading. Feel free to download the Slides on Grading and Hints for Presentations presented during this meeting.

Topics

The seminar topics are:

  1. The Filtering Problem in Discrete Time
  2. The Filtering Problem in Continuous Time and the Kalman Filter
  3. Continuous Time Markov Chains and the Wonham Filter
  4. Parameter Estimation and the Wonham Filter
  5. Parameter Uncertainty in the Kalman Filter
  6. Filter-Based Stochastic Volatility
  7. Portfolio Optimization in Hidden Markov Models
  8. Portfolio Optimization under Partial Information with Gaussian Drift
  9. Portfolio Optimization under Partial Information and Expert Opinions
  10. Randomization in Control Problems with Partial Information

For more information on the individual topics you can consult the slides on The Stochastic Filtering Problem presented during the first preliminary meeting.

Literature

The literature can be downloaded here: