List of Contributors xiii -- Preface xv -- 1 Overview 1 /Ali N. Akansu, Sanjeev R. Kulkarni, and Dmitry Malioutov -- 1.1 Introduction 1 -- 1.2 A Bird's-Eye View of Finance 2 -- 1.2.1 Trading and Exchanges 4 -- 1.2.2 Technical Themes in the Book 5 -- 1.3 Overview of the Chapters 6 -- 1.3.1 Chapter 2: "Sparse Markowitz Portfolios" by Christine De Mol 6 -- 1.3.2 Chapter 3: "Mean-Reverting Portfolios: Tradeoffs between Sparsity and Volatility" by Marco Cuturi and Alexandre d'Aspremont 7 -- 1.3.3 Chapter 4: "Temporal Causal Modeling" by Prabhanjan Kambadur, Aurelie C. Lozano, and Ronny Luss 7 -- 1.3.4 Chapter 5: "Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process" by Mustafa U. Torun, Onur Yilmaz and Ali N. Akansu 7 -- 1.3.5 Chapter 6: "Approaches to High-Dimensional Covariance and Precision Matrix Estimation" by Jianqing Fan, Yuan Liao, and Han Liu 7 -- 1.3.6 Chapter 7: "Stochastic Volatility: Modeling and Asymptotic Approaches to Option Pricing and Portfolio Selection" by Matthew Lorig and Ronnie Sircar 7 -- 1.3.7 Chapter 8: "Statistical Measures of Dependence for Financial Data" by David S. Matteson, Nicholas A. James, and William B. Nicholson 8 -- 1.3.8 Chapter 9: "Correlated Poisson Processes and Their Applications in Financial Modeling" by Alexander Kreinin 8 -- 1.3.9 Chapter 10: "CVaR Minimizations in Support Vector Machines" by Junya Gotoh and Akiko Takeda 8 -- 1.3.10 Chapter 11: "Regression Models in Risk Management" by Stan Uryasev 8 -- 1.4 Other Topics in Financial Signal Processing and Machine Learning 9 -- References 9 -- 2 Sparse Markowitz Portfolios 11 /Christine De Mol -- 2.1 Markowitz Portfolios 11 -- 2.2 Portfolio Optimization as an Inverse Problem: The Need for Regularization 13 -- 2.3 Sparse Portfolios 15 -- 2.4 Empirical Validation 17 -- 2.5 Variations on the Theme 18 -- 2.5.1 Portfolio Rebalancing 18 -- 2.5.2 Portfolio Replication or Index Tracking 19 -- 2.5.3 Other Penalties and Portfolio Norms 19 -- 2.6 Optimal Forecast Combination 20.

Acknowlegments 21 -- References 21 -- 3 Mean-Reverting Portfolios 23 /Marco Cuturi and Alexandre d'Aspremont -- 3.1 Introduction 23 -- 3.1.1 Synthetic Mean-Reverting Baskets 24 -- 3.1.2 Mean-Reverting Baskets with Sufficient Volatility and Sparsity 24 -- 3.2 Proxies for Mean Reversion 25 -- 3.2.1 Related Work and Problem Setting 25 -- 3.2.2 Predictability 26 -- 3.2.3 Portmanteau Criterion 27 -- 3.2.4 Crossing Statistics 28 -- 3.3 Optimal Baskets 28 -- 3.3.1 Minimizing Predictability 29 -- 3.3.2 Minimizing the Portmanteau Statistic 29 -- 3.3.3 Minimizing the Crossing Statistic 29 -- 3.4 Semidefinite Relaxations and Sparse Components 30 -- 3.4.1 A Semidefinite Programming Approach to Basket Estimation 30 -- 3.4.2 Predictability 30 -- 3.4.3 Portmanteau 31 -- 3.4.4 Crossing Stats 31 -- 3.5 Numerical Experiments 32 -- 3.5.1 Historical Data 32 -- 3.5.2 Mean-reverting Basket Estimators 33 -- 3.5.3 Jurek and Yang (2007) Trading Strategy 33 -- 3.5.4 Transaction Costs 33 -- 3.5.5 Experimental Setup 36 -- 3.5.6 Results 36 -- 3.6 Conclusion 39 -- References 39 -- 4 Temporal Causal Modeling 41 /Prabhanjan Kambadur, Aurelie C. Lozano, and Ronny Luss -- 4.1 Introduction 41 -- 4.2 TCM 46 -- 4.2.1 Granger Causality and Temporal Causal Modeling 46 -- 4.2.2 Grouped Temporal Causal Modeling Method 47 -- 4.2.3 Synthetic Experiments 49 -- 4.3 Causal Strength Modeling 51 -- 4.4 Quantile TCM (Q-TCM) 52 -- 4.4.1 Modifying Group OMP for Quantile Loss 52 -- 4.4.2 Experiments 53 -- 4.5 TCM with Regime Change Identification 55 -- 4.5.1 Model 56 -- 4.5.2 Algorithm 58 -- 4.5.3 Synthetic Experiments 60 -- 4.5.4 Application: Analyzing Stock Returns 62 -- 4.6 Conclusions 63 -- References 64 -- 5 Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process 67 /Mustafa U. Torun, Onur Yilmaz, and Ali N. Akansu -- 5.1 Introduction 67 -- 5.2 Mathematical Definitions 68 -- 5.2.1 Discrete AR(1) Stochastic Signal Model 68 -- 5.2.2 Orthogonal Subspace 69 -- 5.3 Derivation of Explicit KLT Kernel for a Discrete AR(1) Process 72.

5.3.1 A Simple Method for Explicit Solution of a Transcendental Equation 73 -- 5.3.2 Continuous Process with Exponential Autocorrelation 74 -- 5.3.3 Eigenanalysis of a Discrete AR(1) Process 76 -- 5.3.4 Fast Derivation of KLT Kernel for an AR(1) Process 79 -- 5.4 Sparsity of Eigen Subspace 82 -- 5.4.1 Overview of Sparsity Methods 83 -- 5.4.2 pdf-Optimized Midtread Quantizer 84 -- 5.4.3 Quantization of Eigen Subspace 86 -- 5.4.4 pdf of Eigenvector 87 -- 5.4.5 Sparse KLT Method 89 -- 5.4.6 Sparsity Performance 91 -- 5.5 Conclusions 97 -- References 97 -- 6 Approaches to High-Dimensional Covariance and Precision Matrix Estimations 100 /Jianqing Fan, Yuan Liao, and Han Liu -- 6.1 Introduction 100 -- 6.2 Covariance Estimation via Factor Analysis 101 -- 6.2.1 Known Factors 103 -- 6.2.2 Unknown Factors 104 -- 6.2.3 Choosing the Threshold 105 -- 6.2.4 Asymptotic Results 105 -- 6.2.5 A Numerical Illustration 107 -- 6.3 Precision Matrix Estimation and Graphical Models 109 -- 6.3.1 Column-wise Precision Matrix Estimation 110 -- 6.3.2 The Need for Tuning-insensitive Procedures 111 -- 6.3.3 TIGER: A Tuning-insensitive Approach for Optimal Precision Matrix Estimation 112 -- 6.3.4 Computation 114 -- 6.3.5 Theoretical Properties of TIGER 114 -- 6.3.6 Applications to Modeling Stock Returns 115 -- 6.3.7 Applications to Genomic Network 118 -- 6.4 Financial Applications 119 -- 6.4.1 Estimating Risks of Large Portfolios 119 -- 6.4.2 Large Panel Test of Factor Pricing Models 121 -- 6.5 Statistical Inference in Panel Data Models 126 -- 6.5.1 Efficient Estimation in Pure Factor Models 126 -- 6.5.2 Panel Data Model with Interactive Effects 127 -- 6.5.3 Numerical Illustrations 130 -- 6.6 Conclusions 131 -- References 131 -- 7 Stochastic Volatility 135 /Matthew Lorig and Ronnie Sircar -- 7.1 Introduction 135 -- 7.1.1 Options and Implied Volatility 136 -- 7.1.2 Volatility Modeling 137 -- 7.2 Asymptotic Regimes and Approximations 141 -- 7.2.1 Contract Asymptotics 142 -- 7.2.2 Model Asymptotics 142.

7.2.3 Implied Volatility Asymptotics 143 -- 7.2.4 Tractable Models 145 -- 7.2.5 Model Coefficient Polynomial Expansions 146 -- 7.2.6 Small "Vol of Vol" Expansion 152 -- 7.2.7 Separation of Timescales Approach 152 -- 7.2.8 Comparison of the Expansion Schemes 154 -- 7.3 Merton Problem with Stochastic Volatility: Model Coefficient Polynomial Expansions 155 -- 7.3.1 Models and Dynamic Programming Equation 155 -- 7.3.2 Asymptotic Approximation 157 -- 7.3.3 Power Utility 159 -- 7.4 Conclusions 160 -- Acknowledgements 160 -- References 160 -- 8 Statistical Measures of Dependence for Financial Data 162 /David S. Matteson, Nicholas A. James, and William B. Nicholson -- 8.1 Introduction 162 -- 8.2 Robust Measures of Correlation and Autocorrelation 164 -- 8.2.1 Transformations and Rank-Based Methods 166 -- 8.2.2 Inference 169 -- 8.2.3 Misspecification Testing 171 -- 8.3 Multivariate Extensions 174 -- 8.3.1 Multivariate Volatility 175 -- 8.3.2 Multivariate Misspecification Testing 176 -- 8.3.3 Granger Causality 176 -- 8.3.4 Nonlinear Granger Causality 177 -- 8.4 Copulas 179 -- 8.4.1 Fitting Copula Models 180 -- 8.4.2 Parametric Copulas 181 -- 8.4.3 Extending beyond Two Random Variables 183 -- 8.4.4 Software 185 -- 8.5 Types of Dependence 185 -- 8.5.1 Positive and Negative Dependence 185 -- 8.5.2 Tail Dependence 187 -- References 188 -- 9 Correlated Poisson Processes and Their Applications in Financial Modeling 191 /Alexander Kreinin -- 9.1 Introduction 191 -- 9.2 Poisson Processes and Financial Scenarios 193 -- 9.2.1 Integrated Market-Credit Risk Modeling 193 -- 9.2.2 Market Risk and Derivatives Pricing 194 -- 9.2.3 Operational Risk Modeling 194 -- 9.2.4 Correlation of Operational Events 195 -- 9.3 Common Shock Model and Randomization of Intensities 196 -- 9.3.1 Common Shock Model 196 -- 9.3.2 Randomization of Intensities 196 -- 9.4 Simulation of Poisson Processes 197 -- 9.4.1 Forward Simulation 197 -- 9.4.2 Backward Simulation 200 -- 9.5 Extreme Joint Distribution 207 -- 9.5.1 Reduction to Optimization Problem 207.

9.5.2 Monotone Distributions 208 -- 9.5.3 Computation of the Joint Distribution 214 -- 9.5.4 On the Frechet-Hoeffding Theorem 215 -- 9.5.5 Approximation of the Extreme Distributions 217 -- 9.6 Numerical Results 219 -- 9.6.1 Examples of the Support 219 -- 9.6.2 Correlation Boundaries 221 -- 9.7 Backward Simulation of the Poisson-Wiener Process 222 -- 9.8 Concluding Remarks 227 -- Acknowledgments 228 -- Appendix A 229 -- A.1 Proof of Lemmas 9.2 and 9.3 229 -- A.1.1 Proof of Lemma 9.2 229 -- A.1.2 Proof of Lemma 9.3 230 -- References 231 -- 10 CVaR Minimizations in Support Vector Machines 233 /Jun-ya Gotoh and Akiko Takeda -- 10.1 What Is CVaR? 234 -- 10.1.1 Definition and Interpretations 234 -- 10.1.2 Basic Properties of CVaR 238 -- 10.1.3 Minimization of CVaR 240 -- 10.2 Support Vector Machines 242 -- 10.2.1 Classification 242 -- 10.2.2 Regression 246 -- 10.3 ¿̧¿-SVMs as CVaR Minimizations 247 -- 10.3.1 ¿̧¿-SVMs as CVaR Minimizations with Homogeneous Loss 247 -- 10.3.2 ¿̧¿-SVMs as CVaR Minimizations with Nonhomogeneous Loss 251 -- 10.3.3 Refining the ¿̧¿-Property 253 -- 10.4 Duality 256 -- 10.4.1 Binary Classification 256 -- 10.4.2 Geometric Interpretation of ¿̧¿-SVM 257 -- 10.4.3 Geometric Interpretation of the Range of ¿̧¿ for ¿̧¿-SVC 258 -- 10.4.4 Regression 259 -- 10.4.5 One-class Classification and SVDD 259 -- 10.5 Extensions to Robust Optimization Modelings 259 -- 10.5.1 Distributionally Robust Formulation 259 -- 10.5.2 Measurement-wise Robust Formulation 261 -- 10.6 Literature Review 262 -- 10.6.1 CVaR as a Risk Measure 263 -- 10.6.2 From CVaR Minimization to SVM 263 -- 10.6.3 From SVM to CVaR Minimization 263 -- 10.6.4 Beyond CVaR 263 -- References 264 -- 11 Regression Models in Risk Management 266 /Stan Uryasev -- 11.1 Introduction 267 -- 11.2 Error and Deviation Measures 268 -- 11.3 Risk Envelopes and Risk Identifiers 271 -- 11.3.1 Examples of Deviation Measures D, Corresponding Risk Envelopes Q, and Sets of Risk Identifiers QD(X) 272 -- 11.4 Error Decomposition in Regression 273.

11.5 Least-Squares Linear Regression 275 -- 11.6 Median Regression 277 -- 11.7 Quantile Regression and Mixed Quantile Regression 281 -- 11.8 Special Types of Linear Regression 283 -- 11.9 Robust Regression 284 -- References, Further Reading, and Bibliography 287 -- Index 289.