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Financial Signal Processing and Machine Learning

Book Description

The modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available. Financial Signal Processing and Machine Learning unifies a number of recent advances made in signal processing and machine learning for the design and management of investment portfolios and financial engineering. This book bridges the gap between these disciplines, offering the latest information on key topics including characterizing statistical dependence and correlation in high dimensions, constructing effective and robust risk measures, and their use in portfolio optimization and rebalancing. The book focuses on signal processing approaches to model return, momentum, and mean reversion, addressing theoretical and implementation aspects. It highlights the connections between portfolio theory, sparse learning and compressed sensing, sparse eigen-portfolios, robust optimization, non-Gaussian data-driven risk measures, graphical models, causal analysis through temporal-causal modeling, and large-scale copula-based approaches.

Key features:

  • Highlights signal processing and machine learning as key approaches to quantitative finance.
  • Offers advanced mathematical tools for high-dimensional portfolio construction, monitoring, and post-trade analysis problems.
  • Presents portfolio theory, sparse learning and compressed sensing, sparsity methods for investment portfolios. including eigen-portfolios, model return, momentum, mean reversion and non-Gaussian data-driven risk measures with real-world applications of these techniques.
  • Includes contributions from leading researchers and practitioners in both the signal and information processing communities, and the quantitative finance community.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. List of Contributors
  5. Preface
  6. Chapter 1: Overview
    1. 1.1 Introduction
    2. 1.2 A Bird's-Eye View of Finance
    3. 1.3 Overview of the Chapters
    4. 1.4 Other Topics in Financial Signal Processing and Machine Learning
    5. References
  7. Chapter 2: Sparse Markowitz Portfolios
    1. 2.1 Markowitz Portfolios
    2. 2.2 Portfolio Optimization as an Inverse Problem: The Need for Regularization
    3. 2.3 Sparse Portfolios
    4. 2.4 Empirical Validation
    5. 2.5 Variations on the Theme
    6. 2.6 Optimal Forecast Combination
    7. Acknowlegments
    8. References
  8. Chapter 3: Mean-Reverting Portfolios
    1. 3.1 Introduction
    2. 3.2 Proxies for Mean Reversion
    3. 3.3 Optimal Baskets
    4. 3.4 Semidefinite Relaxations and Sparse Components
    5. 3.5 Numerical Experiments
    6. 3.6 Conclusion
    7. References
  9. Chapter 4: Temporal Causal Modeling
    1. 4.1 Introduction
    2. 4.2 TCM
    3. 4.3 Causal Strength Modeling
    4. 4.4 Quantile TCM (Q-TCM)
    5. 4.5 TCM with Regime Change Identification
    6. 4.6 Conclusions
    7. References
  10. Chapter 5: Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process
    1. 5.1 Introduction
    2. 5.2 Mathematical Definitions
    3. 5.3 Derivation of Explicit KLT Kernel for a Discrete AR(1) Process
    4. 5.4 Sparsity of Eigen Subspace
    5. 5.5 Conclusions
    6. References
  11. Chapter 6: Approaches to High-Dimensional Covariance and Precision Matrix Estimations
    1. 6.1 Introduction
    2. 6.2 Covariance Estimation via Factor Analysis
    3. 6.3 Precision Matrix Estimation and Graphical Models
    4. 6.4 Financial Applications
    5. 6.5 Statistical Inference in Panel Data Models
    6. 6.6 Conclusions
    7. References
  12. Chapter 7: Stochastic Volatility
    1. 7.1 Introduction
    2. 7.2 Asymptotic Regimes and Approximations
    3. 7.3 Merton Problem with Stochastic Volatility: Model Coefficient Polynomial Expansions
    4. 7.4 Conclusions
    5. Acknowledgements
    6. References
  13. Chapter 8: Statistical Measures of Dependence for Financial Data
    1. 8.1 Introduction
    2. 8.2 Robust Measures of Correlation and Autocorrelation
    3. 8.3 Multivariate Extensions
    4. 8.4 Copulas
    5. 8.5 Types of Dependence
    6. References
  14. Chapter 9: Correlated Poisson Processes and Their Applications in Financial Modeling
    1. 9.1 Introduction
    2. 9.2 Poisson Processes and Financial Scenarios
    3. 9.3 Common Shock Model and Randomization of Intensities
    4. 9.4 Simulation of Poisson Processes
    5. 9.5 Extreme Joint Distribution
    6. 9.6 Numerical Results
    7. 9.7 Backward Simulation of the Poisson–Wiener Process
    8. 9.8 Concluding Remarks
    9. Acknowledgments
    10. Appendix A
    11. References
  15. Chapter 10: CVaR Minimizations in Support Vector Machines
    1. 10.1 What Is CVaR?
    2. 10.2 Support Vector Machines
    3. 10.3 -SVMs as CVaR Minimizations
    4. 10.4 Duality
    5. 10.5 Extensions to Robust Optimization Modelings
    6. 10.6 Literature Review
    7. References
  16. Chapter 11: Regression Models in Risk Management
    1. 11.1 Introduction
    2. 11.2 Error and Deviation Measures
    3. 11.3 Risk Envelopes and Risk Identifiers
    4. 11.4 Error Decomposition in Regression
    5. 11.5 Least-Squares Linear Regression
    6. 11.6 Median Regression
    7. 11.7 Quantile Regression and Mixed Quantile Regression
    8. 11.8 Special Types of Linear Regression
    9. 11.9 Robust Regression
    10. References, Further Reading, and Bibliography
  17. Index
  18. End User License Agreement