Current research

Portfolio theory

Since works of Mandelbrot and Taleb there is a strong empirical indication that returns of the assets are generally not normally distributed.

The Levy stable distribution, which is often proposed to correctly describe the asset returns, is difficult to fit correctly to market data using the known fitting methods. Also the infiniteness of the variance of such distributions, which is believed to represent the the risk in financial markets, represents an open problem of redefining the risk.

The “brute force” approach, i. e. portfolio optimization based on empirical asset return distributions, leads to unbearable computational power requirements for already not very large number of assets in the portfolio. Moreover, empirical distributions lead to systematic underestimation of “catastrophes” (rare events) since real asset return samples are always finite.

Our team of scientists is currently working on a generalization of the well known mean - variance minimization model of the efficient portfolio.

Our effort is aimed to the adaptation of the model to correctly take into account also higher statistical moments (like skewness and kurtosis) than just the first two (mean and variance). Such an approach should be able to cope with the asymmetry of the empirical return distribution.

Multi-model sequential prediction

The project development tasks are focused on discrete random sequence prediction and generally work with binary context-tree weighting predictors as well as derived modifications of context-tree weighting. The research is undertaken in specific areas of multi-model and hierarchical source structures to investigate individual source coding algorithms for context dependent symbol prediction, where context tree sources are preferred structures to give possible different probability of emitting symbols. Of particular interest are also methods that allow parallel implementation of context-tree weighting as well as clustering methods related to learning from finite samples interval sets with known cross correlation. The terminal objectives are application oriented computational methods for classification of random sequences with performance degradation and occurrence probability evaluation.