The Application of Stochastic Bifurcation Theory to the Early Detection of Economic Bubbles

The present research is devoted to the application of stochastic bifurcation theory to the early detection of economic bubbles. A nonlinear random dynamical system with the possible appearance of stochastic P-bifurcations with a fat-tailed probability density function is deduced. The possibility of application of chaotic bifurcation theory to the early detection of culminations of economic bubbles is investigated by the example of dot-com bubbles. For the increments of NASDAQ it is shown that the criterion of reaching the culmination for dot-com bubbles is a formation of a bimodal distribution with the subsequent conversion to a unimodal distribution as a result of codimension one P-bifurcation - a triple equilibrium point.