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Active Portfolio Management Using Stochastic Programming

abstract 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.
   
keywords stochastic programming, portfolio selection, approximation scheme, mean blur, data analysis
   
partner
type applied research project
status ongoing
start of project 2006
end of project 2007
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contact Daniel Kuhn