Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009 (Lecture Notes in Statistics, 198)

Foreword
Preface
Contents
Contributors
Part I Surveys
	1 Copula Theory: An Introduction
		Fabrizio Durante and Carlo Sempi
			1.1 Historical Introduction
				1.1.1 Outline
			1.2 Preliminaries on Random Variables and Distribution Functions
			1.3 Copulas: Definitions and Basic Properties
			1.4 Sklar\'s Theorem
			1.5 Copulas and Random Vectors
			1.6 Families of Copulas
				1.6.1 Elliptical Copulas
				1.6.2 Archimedean Copulas
				1.6.3 EFGM Copulas
			1.7 Constructions of Copulas
				1.7.1 Copulas with Given Lower Dimensional Marginals
				1.7.2 Copula-to-Copula Transformations
				1.7.3 Geometric Constructions of Copulas
			1.8 Copula Theory: What\'s the Future?
			References
	2 Dynamic Modeling of Dependence in Finance via Copulae Between Stochastic Processes
		Tomasz R. Bielecki, Jacek Jakubowski and Mariusz Niewegłowski
			2.1 Introduction
			2.2 Lévy Copulae
			2.3 Semimartingale Copulae
				2.3.1 Copulae for Special Semimartingales
				2.3.2 Consistent Semimartingale Copulae
			2.4 Markov Copulae
				2.4.1 Consistent Markov Processes
				2.4.2 Markov Copulae: Generator Approach
				2.4.3 Markov Copulae: Symbolic Approach
			2.5 Applications in Finance
				2.5.1 Pricing Rating-Triggered Step-Up Bonds via Simulation
				2.5.2 Model Calibration and Pricing
			References
	3 Copula Estimation
		Barbara Choros, Rustam Ibragimov and Elena Permiakova
			3.1 Introduction
			3.2 Copula Estimation: Random Samples with Dependent Marginals
				3.2.1 Parametric Models: Maximum Likelihood Methods and Inference from Likelihoods for Margins
				3.2.2 Semiparametric Estimation
				3.2.3 Nonparametric Inference and Empirical Copula Processes
			3.3 Copula-Based Time Series and Their Estimation
				3.3.1 Copula-Based Characterizations for (Higher-Order) Markov Processes
				3.3.2 Parametric and Semiparametric Copula Estimation Methods for Markov Processes
				3.3.3 Nonparametric Copula Inference for Time Series
				3.3.4 Dependence Properties of Copula-Based Time Series
			3.4 Further Copula Inference Methods
			3.5 Empirical Applications
			References
	4 Pair-Copula Constructions of Multivariate Copulas
		Claudia Czado
			4.1 Introduction
			4.2 Pair Copula Constructions of D-Vine, Canonical and Regular Vine Distributions
				4.2.1 Pair-Copula Constructions of D-Vine and Canonical Vine Distributions
				4.2.2 Regular Vines Distributions and Copulas
			4.3 Estimation Methods for Regular Vine Copulas
			4.4 Model Selection Among Vine Specifications
			4.5 Applications of Vine Distributions
			4.6 Summary and Open Problems
			References
	5 Risk Aggregation
		Paul Embrechts and Giovanni Puccetti
			5.1 Motivations and Preliminaries
				5.1.1 The Mathematical Framework
			5.2 Bounds for Functions of Risks: The Coupling-Dual Approach
				5.2.1 Application 1: Bounding Value-at-Risk
				5.2.2 Application 2: Supermodular Functions
			5.3 The Calculation of the Distribution of the Sum of Risks
				5.3.1 Open Problems
			References
	6 Extreme-Value Copulas
		Gordon Gudendorf and Johan Segers
			6.1 Introduction
			6.2 Foundations
			6.3 Parametric Models
				6.3.1 Logistic Model or Gumbel--Hougaard Copula
				6.3.2 Negative Logistic Model or Galambos Copula
				6.3.3 Hüsler--Reiss Model
				6.3.4 The t-EV Copula
			6.4 Dependence Coefficients
			6.5 Estimation
				6.5.1 Parametric Estimation
				6.5.2 Nonparametric Estimation
			6.6 Further Reading
			References
	7 Construction and Sampling of Nested Archimedean Copulas
		Marius Hofert
			7.1 Introduction
			7.2 Nested Archimedean Copulas
			7.3 A Sufficient Nesting Condition
			7.4 Construction of Nested Archimedean Copulas
			7.5 Sampling Nested Archimedean Copulas
			7.6 Conclusion
			References
	8  Tail Behaviour of Copulas
		Piotr Jaworski
			8.1 Introduction
			8.2  Tail Expansions of Copulas
				8.2.1  Characterization and Properties of Leading Parts
				8.2.2  Relatively Invariant Measures on [0,)n
			8.3  Examples of Tail Expansions
				8.3.1 Homogeneous Copulas
				8.3.2 Diagonal Copulas
				8.3.3 Absolutely Continuous Copulas
				8.3.4 Archimedean Copulas
				8.3.5 Multivariate Extreme Value Copulas
			8.4 Applications
				8.4.1 Tail Conditional Copulas
				8.4.2 Extreme Value Copulas of a Given Copula
				8.4.3 Regularly Varying Random Vectors with a Given Copula
				8.4.4 Value at Risk
			References
	9 Copulae in Reliability Theory  (Order Statistics, Coherent Systems)
		Tomasz Rychlik
			9.1 Coherent Systems
			9.2 Signatures
				9.2.1 Components with i.i.d. Lifetimes
				9.2.2 Mixed Systems
				9.2.3 Components with Exchangeable Lifetimes
			9.3 Bounds for Exchangeable Lifetime Components
				9.3.1 Distribution Bounds
				9.3.2 Expectation Bounds
			9.4 Characterizations of k-Out-of-n System Lifetime Distributions
				9.4.1 General Copula Joint Distribution
				9.4.2 Absolute Continuous Copula Joint Distribution
				9.4.3 Variance Bounds
			9.5 Final Remarks
			References
	10 Copula-Based Measures of Multivariate Association
		Friedrich Schmid, Rafael Schmidt, Thomas Blumentritt,   Sandra Gaißer and Martin Ruppert
			10.1 Introduction and Definitions
			10.2 Aspects of Multivariate Association
			10.3 Multivariate Generalizations of Spearman\'s Rho, Kendall\'s Tau, Blomqvist\'s Beta, and Gini\'s Gamma
				10.3.1 Spearman\'s Rho
				10.3.2 Kendall\'s Tau
				10.3.3 Blomqvist\'s Beta
				10.3.4 Gini\'s Gamma
			10.4 Information-Based Measures of Multivariate Association
			10.5 Measures of Multivariate Association Based on Lp-Distances
				10.5.1 2 as a L2-Distance-Based Measure
				10.5.2  as a L1-Distance-Based Measure
				10.5.3  as a L-Distance-Based Measure
			10.6 Multivariate Tail Dependence
			References
	11 Semi-Copulas and Interpretations of Coincidences Between Stochastic Dependence and Ageing
		Fabio Spizzichino
			11.1 Introduction
			11.2 Univariate Ageing and Dependence Properties of Archimedean Semi-Copulas
			11.3 Dependence and Univariate Ageing in Schur-Constant Models
			11.4 Level Curves, B functions, Duality, and Interpretation of Coincidence Between Ageing and Dependence
			11.5 Summary and Concluding Remarks
			References
Part II Contributed Papers
	12 A Copula-Based Model for Spatial and Temporal Dependence of Equity Markets
		Umberto Cherubini, Fabio Gobbi, Sabrina Mulinacci and Silvia Romagnoli
			12.1 Introduction
			12.2 A market Model in Discrete Time
			12.3 The Martingale Property
			12.4 Applications
				12.4.1 Multivariate Digital Options
				12.4.2 Basket and Spread Options
			References
	13 Nonparametric and Semiparametric Bivariate Modeling of Petrophysical Porosity-Permeability Dependence from Well Log Data
		Arturo Erdely and Martin Diaz-Viera
			13.1 Introduction
			13.2 Methodology
			13.3 Data Analysis
			13.4 Final Remarks
			References
	14 Testing Under the Extended Koziol-Green Model
		Auguste Gaddah and Roel Braekers
			14.1 Introduction
			14.2 Asymptotic Results
			14.3 Test Statistics
			14.4 Data Example: Survival with Malignant Melanoma
			References
	15 Parameter Estimation and Application of the Multivariate Skew t-Copula
		Tõnu Kollo Gaida Pettere
			15.1 Introduction
			15.2 Preliminary Notions and Notation
			15.3 Construction of a Skew t-Copula
			15.4 Parameter Estimation
			15.5 Simulation
			15.6 Application
			References
	16 On Analytical Similarities of Archimedean and Exchangeable Marshall-Olkin Copulas
		Jan-Frederik Mai and Matthias Scherer
			16.1 Introduction
			16.2 Complete Monotonicity and d-Monotonicity
				16.2.1 Definitions and Examples
				16.2.2 Probabilistic Interpretations
				16.2.3 d-Monotonicity
			16.3 Probabilistic Models and Sampling
				16.3.1 The Completely Monotone Case
				16.3.2 The Proper d-Monotone Case
			References
	17 Relationships Between Archimedean Copulas and Morgenstern Utility Functions
		Jaap Spreeuw
			17.1 Introduction
			17.2 Archimedean Copulas
			17.3 Utility Functions
			17.4 Relationships Between Properties of Utility Functions and Properties of Generators
			17.5 Examples
				17.5.1 Classical Cases
				17.5.2 The HARA Family
				17.5.3 The Expo Power Utility
				17.5.4 Other Examples of Decreasing Absolute Risk Aversion (DARA) as in Pratt [9]
			17.6 Conclusion
			References
		Index