Mathematical Risk Analysis

Transcription

1 Springer Series in Operations Research and Financial Engineering Mathematical Risk Analysis Dependence, Risk Bounds, Optimal Allocations and Portfolios Bearbeitet von Ludger Rüschendorf 1. Auflage Buch. xii, 408 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 789 g Weitere Fachgebiete > Mathematik > Operational Research > Finanz- und Versicherungsmathematik schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents Part I Stochastic Dependence and Extremal Risk 1 Copulas, Sklar s Theorem, and Distributional Transform Sklar s Theorem and the Distributional Transform Copula Models and Copula Constructions Some Classes of Copulas Copulas and L 2 -Projections Multivariate Distributional and Quantile Transform Pair Copula Construction of Copula Models Applications of the Distributional Transform Application to Stochastic Ordering Optimal Couplings Identification and Goodness of Fit Tests Empirical Copula Process and Empirical Dependence Function Multivariate and Overlapping Marginals Generalized Fréchet Class Copulas with Given Independence Structure Copulas, Overlapping Marginals, and L 2 -Projections Fréchet Classes, Risk Bounds, and Duality Theory Dual Representation of Generalized Fréchet Bounds Fréchet Bounds Comonotonicity and Extremal Risk Convex Order, Excess of Loss, and Comonotonicity Convex Order and Comonotonicity Schur Order and Rearrangements Rearrangements and Excess of Loss Integral Orders and F -Diffusions ix

3 x Contents 4 Bounds for the Distribution Function and Value at Risk of the Joint Portfolio Standard Bounds Conditional Moment Method Dual Bounds Restrictions on the Dependence Structure Restriction to Positive Dependent Risk Vectors Higher Order Marginals A Reduction Principle and Bonferroni Type Bounds The Conditioning Method Reduction Bounds for the Joint Portfolio in General Marginal Systems Dependence Orderings of Risk Vectors and Portfolios Positive Orthant Dependence and Supermodular Ordering Association, Conditional Increasing Vectors, and Positive Supermodular Dependence Directionally Convex Order Basic Properties of the Directionally Convex Order Further Criteria for dcx Directionally Convex Order in Functional Models Dependence Orderings in Models with Multivariate Marginals Part II Risk Measures and Worst Case Portfolios 7 Risk Measures for Real Risks Some Classes of Risk Measures for Real Variables Basic Properties of Risk Measures Examples of Risk Measures Representation and Continuity Properties of Convex Risk Measures on L p -Spaces Convex Duality and Continuity Results Representation of Coherent and Convex Risk Measures on L p Continuity Results for Risk Measures on L p Risk Measures for Portfolio Vectors Basic Properties of Portfolio Risk Measures Classes of Examples of Portfolio Risk Measures Aggregation Type Risk Measures Multivariate Distortion and Quantile-Type Risk Measures

4 Contents xi 8.3 Representation and Continuity of Convex Risk Measures on L p d Law Invariant Convex Risk Measures on L p and Optimal d Mass Transportation Law Invariant Risk Measures and Optimal Mass Transportation Multivariate Comonotonicity and the n-coupling Problem Worst Case Portfolio Vectors and Diversification Effects Examples of Worst Case Risk Portfolios and Worst Case Diversification Effects Part III Optimal Risk Allocation 10 Optimal Allocations and Pareto Equilibrium Pareto Equilibrium and Related Risk Measures in the Coherent Case Optimal Allocations Under Admissibility Restrictions Pareto Equilibrium for Convex Risk Measures Pareto Optimality, Comonotonicity, and Existence of Optimal Allocations Characterization and Examples of Optimal Risk Allocations for Convex Risk Functionals Inf-Convolution and Convex Conjugates Characterization of Optimal Allocations Examples of Optimal Risk Allocations Expected Risk Functionals Dilated Risk Functionals Average Value at Risk and Stop-Loss Contracts Mean Variance Versus Standard Deviation Risk Functionals Optimal Allocation of Risk Vectors Characterization of Optimal Allocations Law Invariant Risk Measures and Comonotonicity Existence of Minimal Risk Allocations Uniqueness of Optimal Allocations Examples of Optimal Allocations The Capital Allocation Problem Optimal Contingent Claims and (Re)insurance Contracts Optimal Contingent Claims Optimal Investment Problems Minimal Demand Problem Optimal (Re)insurance Contracts Optimality of Stop-Loss Contracts Optimal Worst Case (Re)insurance Contracts

5 xii Contents Part IV Optimal Portfolios and Extreme Risks 13 Optimal Portfolio Diversification w.r.t. Extreme Risks Heavy-Tailed Portfolios and Multivariate Regular Variation Extreme Risk Index and Portfolio Diversification Estimation of the Extreme Risk Index and the Optimal Portfolio Asymptotic Normality of b Application to Risk Minimization Ordering of Multivariate Risk Models with Respect to Extreme Portfolio Losses Asymptotic Portfolio Loss Ordering Characterization of apl in Multivariate Regularly Varying Models Multivariate Regular Variation Ordering of Canonical Spectral Measures Unbalanced Tails Relations to the Convex and Supermodular Order Examples of apl-ordering References List of Symbols Index