Quantitative analysis of financial system fragility based on manifold curvature

Manifold curvature is an intrinsic attribute of a dynamical system. By analyzing curvature characteristics of embedding attractor manifold, resistance and resilience of financial dynamic system are investigated in the face of disturbances, thus system fragility is discussed quantitatively from a systemic perspective. First, financial time series data are reconstructed into a high-dimensional phase space, topologically equivalent to its original dynamical system. Then, manifold learning is employed to extract attractor manifold embedding in financial dynamic system. Last, by numerical calculation, the manifold curvature is obtained and further visualized with spatial mapping. In empirical study, Shanghai Composite Index and Dow Jones Industrial Index are adopted as experimental data, and then a more comprehensive understanding about financial systems fragility is obtained by exploring the dynamical properties related to manifold curvature.