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Preface | |
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Risk in Perspective | |
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Risk | |
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Risk and Randomness | |
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Financial Risk | |
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Measurement and Management | |
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A Brief History of Risk Management | |
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From Babylon to Wall Street | |
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The Road to Regulation | |
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The New Regulatory Framework | |
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Basel II | |
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Solvency 2 | |
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Why Manage Financial Risk? | |
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A Societal View | |
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The Shareholder's View | |
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Economic Capital | |
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Quantitative Risk Management | |
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The Nature of the Challenge | |
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QRM for the Future | |
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Basic Concepts in Risk Management | |
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Risk Factors and Loss Distributions | |
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General Definitions | |
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Conditional and Unconditional Loss Distribution | |
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Mapping of Risks: Some Examples | |
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Risk Measurement | |
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Approaches to Risk Measurement | |
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Value-at-Risk | |
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Further Comments on VaR | |
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Other Risk Measures Based on Loss Distributions | |
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Standard Methods for Market Risks | |
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Variance-Covariance Method | |
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Historical Simulation | |
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Monte Carlo | |
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Losses over Several Periods and Scaling | |
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Backtesting | |
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An Illustrative Example | |
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Multivariate Models | |
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Basics of Multivariate Modelling | |
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Random Vectors and Their Distributions | |
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Standard Estimators of Covariance and Correlation | |
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The Multivariate Normal Distribution | |
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Testing Normality and Multivariate Normality | |
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Normal Mixture Distributions | |
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Normal Variance Mixtures | |
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Normal Mean-Variance Mixtures | |
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Generalized Hyperbolic Distributions | |
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Fitting Generalized Hyperbolic Distributions to Data | |
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Empirical Examples | |
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Spherical and Elliptical Distributions | |
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Spherical Distributions | |
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Elliptical Distributions | |
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Properties of Elliptical Distributions | |
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Estimating Dispersion and Correlation | |
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Testing for Elliptical Symmetry | |
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Dimension Reduction Techniques | |
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Factor Models | |
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Statistical Calibration Strategies | |
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Regression Analysis of Factor Models | |
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Principal Component Analysis | |
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Financial Time Series | |
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Empirical Analyses of Financial Time Series | |
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Stylized Facts | |
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Multivariate Stylized Facts | |
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Fundamentals of Time Series Analysis | |
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Basic Definitions | |
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ARMA Processes | |
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Analysis in the Time Domain | |
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Statistical Analysis of Time Series | |
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Prediction | |
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GARCH Models for Changing Volatility | |
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ARCH Processes | |
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GARCH Processes | |
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Simple Extensions of the GARCH Model | |
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Fitting GARCH Models to Data | |
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Volatility Models and Risk Estimation | |
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Volatility Forecasting | |
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Conditional Risk Measurement | |
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Backtesting | |
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Fundamentals of Multivariate Time Series | |
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Basic Definitions | |
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Analysis in the Time Domain | |
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Multivariate ARMA Processes | |
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Multivariate GARCH Processes | |
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General Structure of Models | |
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Models for Conditional Correlation | |
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Models for Conditional Covariance | |
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Fitting Multivariate GARCH Models | |
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Dimension Reduction in MGARCH | |
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MGARCH and Conditional Risk Measurement | |
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Copulas and Dependence | |
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Copulas | |
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Basic Properties | |
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Examples of Copulas | |
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Meta Distributions | |
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Simulation of Copulas and Meta Distributions | |
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Further Properties of Copulas | |
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Perfect Dependence | |
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Dependence Measures | |
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Linear Correlation | |
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Rank Correlation | |
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Coefficients of Tail Dependence | |
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Normal Mixture Copulas | |
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Tail Dependence | |
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Rank Correlations | |
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Skewed Normal Mixture Copulas | |
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Grouped Normal Mixture Copulas | |
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Archimedean Copulas | |
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Bivariate Archimedean Copulas | |
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Multivariate Archimedean Copulas | |
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Non-exchangeable Archimedean Copulas | |
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Fitting Copulas to Data | |
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Method-of-Moments using Rank Correlation | |
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Forming a Pseudo-Sample from the Copula | |
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Maximum Likelihood Estimation | |
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Aggregate Risk | |
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Coherent Measures of Risk | |
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The Axioms of Coherence | |
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Value-at-Risk | |
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Coherent Risk Measures Based on Loss Distributions | |
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Coherent Risk Measures as Generalized Scenarios | |
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Mean-VaR Portfolio Optimization | |
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Bounds for Aggregate Risks | |
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The General Frechet Problem | |
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The Case of VaR | |
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Capital Allocation | |
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The Allocation Problem | |
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The Euler Principle and Examples | |
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Economic Justification of the Euler Principle | |
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Extreme Value Theory | |
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Maxima | |
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Generalized Extreme Value Distribution | |
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Maximum Domains of Attraction | |
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Maxima of Strictly Stationary Time Series | |
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The Block Maxima Method | |
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Threshold Exceedances | |
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Generalized Pareto Distribution | |
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Modelling Excess Losses | |
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Modelling Tails and Measures of Tail Risk | |
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The Hill Method | |
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Simulation Study of EVT Quantile Estimators | |
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Conditional EVT for Financial Time Series | |
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Tails of Specific Models | |
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Domain of Attraction of Frechet Distribution | |
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Domain of Attraction of Gumbel Distribution | |
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Mixture Models | |
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Point Process Models | |
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Threshold Exceedances for Strict White Noise | |
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The POT Model | |
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Self-Exciting Processes | |
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A Self-Exciting POT Model | |
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Multivariate Maxima | |
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Multivariate Extreme Value Copulas | |
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Copulas for Multivariate Minima | |
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Copula Domains of Attraction | |
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Modelling Multivariate Block Maxima | |
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Multivariate Threshold Exceedances | |
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Threshold Models Using EV Copulas | |
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Fitting a Multivariate Tail Model | |
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Threshold Copulas and Their Limits | |
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Credit Risk Management | |
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Introduction to Credit Risk Modelling | |
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Credit Risk Models | |
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The Nature of the Challenge | |
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Structural Models of Default | |
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The Merton Model | |
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Pricing in Merton's Model | |
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The KMV Model | |
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Models Based on Credit Migration | |
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Multivariate Firm-Value Models | |
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Threshold Models | |
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Notation for One-Period Portfolio Models | |
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Threshold Models and Copulas | |
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Industry Examples | |
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Models Based on Alternative Copulas | |
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Model Risk Issues | |
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The Mixture Model Approach | |
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One-Factor Bernoulli Mixture Models | |
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CreditRisk+ | |
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Asymptotics for Large Portfolios | |
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Threshold Models as Mixture Models | |
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Model-Theoretic Aspects of Basel II | |
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Model Risk Issues | |
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Monte Carlo Methods | |
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Basics of Importance Sampling | |
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Application to Bernoulli-Mixture Models | |
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Statistical Inference for Mixture Models | |
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Motivation | |
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Exchangeable Bernoulli-Mixture Models | |
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Mixture Models as GLMMs | |
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One-Factor Model with Rating Effect | |
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Dynamic Credit Risk Models | |
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Credit Derivatives | |
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Overview | |
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Single-Name Credit Derivatives | |
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Portfolio Credit Derivatives | |
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Mathematical Tools | |
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Random Times and Hazard Rates | |
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Modelling Additional Information | |
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Doubly Stochastic Random Times | |
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Financial and Actuarial Pricing of Credit Risk | |
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Physical and Risk-Neutral Probability Measure | |
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Risk-Neutral Pricing and Market Completeness | |
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Martingale Modelling | |
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The Actuarial Approach to Credit Risk Pricing | |
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Pricing with Doubly Stochastic Default Times | |
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Recovery Payments of Corporate Bonds | |
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The Model | |
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Pricing Formulas | |
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Applications | |
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Affine Models | |
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Basic Results | |
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The CIR Square-Root Diffusion | |
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Extensions | |
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Conditionally Independent Defaults | |
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Reduced-Form Models for Portfolio Credit Risk | |
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Conditionally Independent Default Times | |
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Examples and Applications | |
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Copula Models | |
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Definition and General Properties | |
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Factor Copula Models | |
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Default Contagion in Reduced-Form Models | |
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Default Contagion and Default Dependence | |
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Information-Based Default Contagion | |
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Interacting Intensities | |
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Operational Risk and Insurance Analytics | |
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Operational Risk in Perspective | |
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A New Risk Class | |
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The Elementary Approaches | |
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Advanced Measurement Approaches | |
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Operational Loss Data | |
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Elements of Insurance Analytics | |
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The Case for Acturaial Methodology | |
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The Total Loss Amount | |
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Approximations and Panjer Recursion | |
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Poisson Mixtures | |
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Tails of Aggregate Loss Distributions | |
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The Homogeneous Poisson Process | |
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Processes Related to the Poisson Process | |
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Appendix | |
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Miscellaneous Definitions and Results | |
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Type of Distribution | |
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Generalized Inverses and Quantiles | |
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Karamata's Theorem | |
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Probability Distributions | |
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Beta | |
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Exponential | |
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F | |
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Gamma | |
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Generalized Inverse Gaussian | |
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Inverse Gamma | |
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Negative Binomial | |
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Pareto | |
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Stable | |
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Likelihood Inference | |
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Maximum Likelihood Estimators | |
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Asymptotic Results: Scalar Parameter | |
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Asymptotic Results: Vector of Parameters | |
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Wald Test and Confidence Intervals | |
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Likelihood Ratio Test and Confidence Intervals | |
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Akaike Information Criterion | |
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References | |
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Index | |