This title uses advanced signal processing technology to measure and analyse risk phenomena of the financial markets. It explains how to scientifically measure, analyse 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 modelling 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. INDICE Part I: Financial Risk Processes 1. Risk: Asset Class, Horizon, and Time 2. Competing Financial Market Hypotheses 3. Stable Scaling Distributions in Finance 4. Persistence of Financial Risk Part II: Financial Risk Measurement 5. Frequency Analysis of Financial Risk 6. Fourier Time - Frequency Analysis of Risk 7. Wavelet Time - Scale Analysis of Risk 8. Multiresolution Analysis of Local Risk Part III: Term Structure Dynamics 9. Chaos: Nonunique Equilibrium Processes 10. Measuring Term Structure Dynamics 11. Financial Turbulence: Measurement and Simulation Part 4: Financial Risk Management 12. Managing VaR and Extreme Values