| Preface | p. vii |
| Introduction | p. 1 |
| Copulas | p. 4 |
| Analytical Properties | p. 7 |
| Sklar's Theorem and Survival Copulas | p. 14 |
| General Sampling Methodology in Low Dimensions | p. 22 |
| Graphical Visualization | p. 26 |
| Concordance Measures | p. 28 |
| Measures of Extremal Dependence | p. 33 |
| General Classifications of Copulas | p. 36 |
| Radial Symmetry | p. 36 |
| Exchangeability | p. 39 |
| Homogeneous Mixture Models | p. 41 |
| Heterogeneous Mixture Models/Hierarchical Models | p. 48 |
| Extreme-Value Copulas | p. 52 |
| Archimedean Copulas | p. 57 |
| Motivation | p. 58 |
| Extendible Archimedean Copulas | p. 61 |
| Kimberling's Result and Bernstein's Theorem | p. 62 |
| Properties of Extendible Archimedean Copulas | p. 65 |
| Constructing Multi-Parametric Families | p. 69 |
| Parametric Families | p. 69 |
| Exchangeable Archimedean Copulas | p. 76 |
| Constructing Exchangeable Archimedean Copulas | p. 82 |
| Sampling Exchangeable Archimedean Copulas | p. 85 |
| Properties of Exchangeable Archimedean Copulas | p. 87 |
| Hierarchical (H-Extendible) Archimedean Copulas | p. 89 |
| Compatibility of Generators | p. 90 |
| Probabilistic Construction and Sampling | p. 91 |
| Properties | p. 93 |
| Examples | p. 95 |
| Other Topics Related to Archimedean Copulas | p. 97 |
| Simulating from the Generator | p. 97 |
| Asymmetrizing Archimedean Copulas | p. 99 |
| Marshall-Olkin Copulas | p. 101 |
| The General Marshall-Olkin Copula | p. 102 |
| Canonical Construction of the MO Distribution | p. 104 |
| Alternative Construction of the MO Distribution | p. 110 |
| Properties of Marshall-Olkin Copulas | p. 118 |
| The Exchangeable Case | p. 122 |
| Reparameterizing Marshall-Olkin Copulas | p. 126 |
| The Inverse Pascal Triangle | p. 129 |
| Efficiently Sampling eMO | p. 131 |
| Hierarchical Extensions | p. 138 |
| The Extendible Case | p. 140 |
| Precise Formulation and Proof of Theorem 3.1 | p. 141 |
| Proof of Theorem 3.2 | p. 146 |
| Efficient Simulation of Lévy-Frailty Copulas | p. 150 |
| Hierarchical (H-Extendible) Lévy-Frailty Copulas | p. 153 |
| Elliptical Copulas | p. 159 |
| Spherical Distributions | p. 161 |
| Elliptical Distributions | p. 166 |
| Parametric Families of Elliptical Distributions | p. 170 |
| Elliptical Copulas | p. 174 |
| Parametric Families of Elliptical Copulas | p. 175 |
| Sampling Algorithms | p. 179 |
| A Generic Sampling Scheme | p. 179 |
| Sampling Important Parametric Families | p. 181 |
| Pair Copula Constructions | p. 185 |
| Introduction to Pair Copula Constructions | p. 186 |
| Copula Construction by Regular Vine Trees | p. 191 |
| Regular Vines | p. 191 |
| Regular Vine Matrices | p. 196 |
| Simulation from Regular Vine Distributions | p. 203 |
| h-Functions for Bivariate Copulas and Then Rotated Versions | p. 204 |
| The Sampling Algorithms | p. 208 |
| Dependence Properties | p. 218 |
| Application | p. 223 |
| Time Series Model for Each Margin | p. 224 |
| Parameter Estimation | p. 224 |
| Forecasting Value at Risk | p. 226 |
| Backtesting Value at Risk | p. 227 |
| Backtest Results | p. 228 |
| Sampling Univariate Random Variables | p. 231 |
| General Aspects of Generating Random Variables | p. 231 |
| Generating Uniformly Distributed Random Variables | p. 232 |
| Quality Criteria for RNG | p. 233 |
| Common Causes of Trouble | p. 234 |
| The Inversion Method | p. 234 |
| Generating Exponentially Distributed Random Numbers | p. 235 |
| Acceptance-Rejection Method | p. 235 |
| Generating Normally Distributed Random Numbers | p. 238 |
| Calculating the Cumulative Normal | p. 238 |
| Generating Normally Distributed Random Numbers via Inversion | p. 238 |
| Generating Normal Random Numbers with Polar Methods | p. 239 |
| Generating Lognormal Random Numbers | p. 240 |
| Generating Gamma-Distributed Random Numbers | p. 240 |
| Generating Gamma-Distributed RNs with ß > 1 | p. 241 |
| Generating Gamma-Distributed RNs with ß < 1 | p. 242 |
| Relations to Other Distributions | p. 243 |
| Generating Chi-Square-Distributed RNs | p. 243 |
| Generating t-Distributed Random Numbers | p. 244 |
| Generating Pareto-Distributed Random Numbers | p. 245 |
| Generating Inverse Gaussian-Distributed Random Numbers | p. 245 |
| Generating Stable-Distributed Random Numbers | p. 246 |
| Generating Discretely Distributed Random Numbers | p. 247 |
| Generating Random Numbers with Geometric and Binomial Distribution | p. 248 |
| Generating Poisson-Distributed Random Numbers | p. 248 |
| The Monte Carlo Method | p. 251 |
| First Aspects of the Monte Carlo Method | p. 251 |
| Variance Reduction Methods | p. 254 |
| Antithetic Variates | p. 255 |
| Antithetic Variates for Radially Symmetric Copulas | p. 257 |
| Control Variates | p. 258 |
| Approximation via a Simpler Dependence Structure | p. 260 |
| Importance Sampling | p. 262 |
| Importance Sampling via Increasing the Dependence | p. 263 |
| Further Comments on Variance Reduction Methods | p. 265 |
| Supplemental Material | p. 267 |
| Validating a Sampling Algorithm | p. 267 |
| Introduction to Lévy Subordinators | p. 268 |
| Compound Poisson Subordinator | p. 272 |
| Gamma Subordinator | p. 274 |
| Inverse Gaussian Subordinator | p. 275 |
| Stable Subordinator | p. 276 |
| Scale Mixtures of Marshall-Olkin Copulas | p. 277 |
| Further Reading | p. 281 |
| Bibliography | p. 283 |
| Index | p. 293 |
| Table of Contents provided by Ingram. All Rights Reserved. |
