Chapter
2.2 Portfolio Optimization as an Inverse Problem: The Need for Regularization
2.5 Variations on the Theme
2.5.1 Portfolio Rebalancing
2.5.2 Portfolio Replication or Index Tracking
2.5.3 Other Penalties and Portfolio Norms
2.6 Optimal Forecast Combination
Chapter 3 Mean-Reverting Portfolios
3.1.1 Synthetic Mean-Reverting Baskets
3.1.2 Mean-Reverting Baskets with Sufficient Volatility and Sparsity
3.2 Proxies for Mean Reversion
3.2.1 Related Work and Problem Setting
3.2.3 Portmanteau Criterion
3.2.4 Crossing Statistics
3.3.1 Minimizing Predictability
3.3.2 Minimizing the Portmanteau Statistic
3.3.3 Minimizing the Crossing Statistic
3.4 Semidefinite Relaxations and Sparse Components
3.4.1 A Semidefinite Programming Approach to Basket Estimation
3.5 Numerical Experiments
3.5.2 Mean-reverting Basket Estimators
3.5.3 Jurek and Yang (2007) Trading Strategy
Chapter 4 Temporal Causal Modeling
4.2.1 Granger Causality and Temporal Causal Modeling
4.2.2 Grouped Temporal Causal Modeling Method
4.2.3 Synthetic Experiments
4.3 Causal Strength Modeling
4.4.1 Modifying Group OMP for Quantile Loss
4.5 TCM with Regime Change Identification
4.5.3 Synthetic Experiments
4.5.4 Application: Analyzing Stock Returns
Chapter 5 Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process
5.2 Mathematical Definitions
5.2.1 Discrete AR(1) Stochastic Signal Model
5.2.2 Orthogonal Subspace
5.3 Derivation of Explicit KLT Kernel for a Discrete AR(1) Process
5.3.1 A Simple Method for Explicit Solution of a Transcendental Equation
5.3.2 Continuous Process with Exponential Autocorrelation
5.3.3 Eigenanalysis of a Discrete AR(1) Process
5.3.4 Fast Derivation of KLT Kernel for an AR(1) Process
5.4 Sparsity of Eigen Subspace
5.4.1 Overview of Sparsity Methods
5.4.2 pdf-Optimized Midtread Quantizer
5.4.3 Quantization of Eigen Subspace
5.4.6 Sparsity Performance
Chapter 6 Approaches to High-Dimensional Covariance and Precision Matrix Estimations
6.2 Covariance Estimation via Factor Analysis
6.2.3 Choosing the Threshold
6.2.5 A Numerical Illustration
6.3 Precision Matrix Estimation and Graphical Models
6.3.1 Column-wise Precision Matrix Estimation
6.3.2 The Need for Tuning-insensitive Procedures
6.3.3 TIGER: A Tuning-insensitive Approach for Optimal Precision Matrix Estimation
6.3.5 Theoretical Properties of TIGER
6.3.6 Applications to Modeling Stock Returns
6.3.7 Applications to Genomic Network
6.4 Financial Applications
6.4.1 Estimating Risks of Large Portfolios
6.4.2 Large Panel Test of Factor Pricing Models
6.5 Statistical Inference in Panel Data Models
6.5.1 Efficient Estimation in Pure Factor Models
6.5.2 Panel Data Model with Interactive Effects
6.5.3 Numerical Illustrations
Chapter 7 Stochastic Volatility
7.1.1 Options and Implied Volatility
7.1.2 Volatility Modeling
7.2 Asymptotic Regimes and Approximations
7.2.1 Contract Asymptotics
7.2.3 Implied Volatility Asymptotics
7.2.5 Model Coefficient Polynomial Expansions
7.2.6 Small "Vol of Vol" Expansion
7.2.7 Separation of Timescales Approach
7.2.8 Comparison of the Expansion Schemes
7.3 Merton Problem with Stochastic Volatility: Model Coefficient Polynomial Expansions
7.3.1 Models and Dynamic Programming Equation
7.3.2 Asymptotic Approximation
Chapter 8 Statistical Measures of Dependence for Financial Data
8.2 Robust Measures of Correlation and Autocorrelation
8.2.1 Transformations and Rank-Based Methods
8.2.3 Misspecification Testing
8.3 Multivariate Extensions
8.3.1 Multivariate Volatility
8.3.2 Multivariate Misspecification Testing
8.3.4 Nonlinear Granger Causality
8.4.1 Fitting Copula Models
8.4.3 Extending beyond Two Random Variables
8.5.1 Positive and Negative Dependence
Chapter 9 Correlated Poisson Processes and Their Applications in Financial Modeling
9.2 Poisson Processes and Financial Scenarios
9.2.1 Integrated Market-Credit Risk Modeling
9.2.2 Market Risk and Derivatives Pricing
9.2.3 Operational Risk Modeling
9.2.4 Correlation of Operational Events
9.3 Common Shock Model and Randomization of Intensities
9.3.2 Randomization of Intensities
9.4 Simulation of Poisson Processes
9.4.2 Backward Simulation
9.5 Extreme Joint Distribution
9.5.1 Reduction to Optimization Problem
9.5.2 Monotone Distributions
9.5.3 Computation of the Joint Distribution
9.5.4 On the Frechet-Hoeffding Theorem
9.5.5 Approximation of the Extreme Distributions
9.6.1 Examples of the Support
9.6.2 Correlation Boundaries
9.7 Backward Simulation of the Poisson-Wiener Process
A.1 Proof of Lemmas 9.2 and 9.3
Chapter 10 CVaR Minimizations in Support Vector Machines
10.1.1 Definition and Interpretations
10.1.2 Basic Properties of CVaR
10.1.3 Minimization of CVaR
10.2 Support Vector Machines
10.3 v-SVMs as CVaR Minimizations
10.3.1 v-SVMs as CVaR Minimizations with Homogeneous Loss
10.3.2 v-SVMs as CVaR Minimizations with Nonhomogeneous Loss
10.3.3 Refining the v-Property
10.4.1 Binary Classification
10.4.2 Geometric Interpretation of v-SVM
10.4.3 Geometric Interpretation of the Range of v for v-SVC
10.4.5 One-class Classification and SVDD
10.5 Extensions to Robust Optimization Modelings
10.5.1 Distributionally Robust Formulation
10.5.2 Measurement-wise Robust Formulation
10.6.1 CVaR as a Risk Measure
10.6.2 From CVaR Minimization to SVM
10.6.3 From SVM to CVaR Minimization
Chapter 11 Regression Models in Risk Management
11.2 Error and Deviation Measures
11.3 Risk Envelopes and Risk Identifiers
11.3.1 Examples of Deviation Measures D, Corresponding Risk Envelopes Q, and Sets of Risk Identifiers DQ(X)
11.4 Error Decomposition in Regression
11.5 Least-Squares Linear Regression
11.7 Quantile Regression and Mixed Quantile Regression
11.8 Special Types of Linear Regression
References, Further Reading, and Bibliography
Financial Signal Processing and Machine Learning
( Wiley - IEEE )
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