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Cooperation with: O. Hryniv (University of Cambridge, UK)
Supported by: DFG-Forschungszentrum ,,Mathematik für Schlüsseltechnologien`` (Research Center ``Mathematics for Key Technologies''), project E1
Description: The main goal of this new project, that is part of the application area E of the DFG Research Center ``Mathematics for Key Technologies'', is to develop and investigate more realistic models for the dynamics of stock prices that take into account the actual trading mechanisms involved in the price evolution. In this way one hopes to bring methods and ideas from the theory of interacting random systems to bear on the theory of price processes in finance ([2]).
An approach based on a Markovian evolution in a space of opinions of traders is presented in the paper [1]. We have developed an interactive simulation tool that allows to experiment with a rather large class of model parameters, and some rather interesting features emerge even with rather simple models involving few parameters. One can, for instance, study the effect of time-dependent changes in parameters (modeling a changing macro-economic environment) on the stock price. For example, the following graph shows the reaction to a sequence of bursts of optimism followed by neutral periods.
It also emerges that one can identify a number of very challenging mathematical problems in the context of interacting particle systems that are relevant and so far little understood. The further development of the model, its numerical and analytical investigation, and comparison of statistical properties of the model price processes with real data, offer interesting perspectives for continued research over the next years.
References:
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