Active Portfolio Management Using Stochastic Programming
Type
applied research project
Start Date
September 1, 2006
End Date
August 31, 2007
Status
ongoing
Keywords
stochastic programming
portfolio selection
approximation scheme
mean blur
data analysis
Description
This research project addresses portfolio selection problems from a stochastic programming perspective. Emphasis is put on a careful modelling of the asset price dynamics. It is assumed that the assets' drift rates are observable only in a limited manner since they are blurred by superposed fluctuations; this phenomenon is referred to as ‘mean blur' in literature. Whenever the portfolio composition is changed, the investor estimates the current drift rates by means of Bayesian techniques (relying only on historic prices and fundamental data). This dynamic updating of estimates is taken account of in a stochastic optimization model. We evaluate the influence of the underlying price processes, the rebalancing frequency, and possible portfolio constraints on the portfolio performance. In order to formulate and (efficiently) solve investment problems of the above type, we have to conduct research in different fields:
- stochastic processes and optimal filtering: modelling of asset price dynamics; the (unobserved) drift rates can be assumed deterministic, mean-reverting, or regime-switching, etc.; corresponding filter equations must be derived;
- stochastic optimization: development and validation of flexible approximation schemes which overcome the curse of dimensionality, construction of arbitrarily tight error bounds;
- statistics and information theory: calibration of different probabilistic models, and evaluation of these models by means of statistical tests.
Portfolio optimization is a prototypical application area of stochastic programming and data analysis. Therefore, we will strive for generalizing our specific findings to broader problem classes in all phases of the proposed research project.
- stochastic processes and optimal filtering: modelling of asset price dynamics; the (unobserved) drift rates can be assumed deterministic, mean-reverting, or regime-switching, etc.; corresponding filter equations must be derived;
- stochastic optimization: development and validation of flexible approximation schemes which overcome the curse of dimensionality, construction of arbitrarily tight error bounds;
- statistics and information theory: calibration of different probabilistic models, and evaluation of these models by means of statistical tests.
Portfolio optimization is a prototypical application area of stochastic programming and data analysis. Therefore, we will strive for generalizing our specific findings to broader problem classes in all phases of the proposed research project.
Leader contributor(s)
Kuhn, Daniel
Funder
Division(s)
Eprints ID
33914