Dynamic instability in generic model of multi-assets markets

We introduce a generic model of a multi-asset financial market, which takes into account the impact of portfolio investment on price dynamics. This captures the fact that financial correlation determine the optimal portfolio but are affected by investment based on it. We show that, under very general conditions, such a feedback on correlations gives rise to an instability when the volume of investment exceeds a critical value. Close to the critical point the model exhibits dynamical correlations very similar to those observed in empirical data.