This new book uses advanced signal processing technology to measure and analyze risk phenomena of the financial markets. It explains how to scientifically measure, analyze and manage non-stationarity and long-term time dependence (long memory) of financial market returns. It studies, in particular, financial crises in persistent financial markets, such as stock, bond and real estate market, and turbulence in antipersistent financial markets, such as anchor currency markets. It uses Windowed Fourier and Wavelet Multiresolution Analysis to measure the degrees of persistence of these complex markets, by computing monofractal Hurst exponents and multifractal singularity spectra. It explains how and why financial crises and financial turbulence may occur in the various markets and why we may have to reconsider the current wave of term structure modeling based on affine models. It also uses these persistence measurements to improve the financial risk management of global investment funds, via numerical simulations of the nonlinear diffusion equations describing the underlying high frequency dynamic pricing processes.