Synopses & Reviews
The author's particular interest in the area of risk measures is to combine this theory with the analysis of dependence properties. The present volume gives an introduction of basic concepts and methods in mathematical risk analysis, in particular of those parts of risk theory that are of special relevance to finance and insurance. Describing the influence of dependence in multivariate stochastic models on risk vectors is the main focus of the text that presents main ideas and methods as well as their relevance to practical applications.
The up-to-date material and logical structure of this volume provides the clarity and orientation needed to gain a solid working knowledge of mathematical risk analysis. It includes a specialized focus on the risk theory deployed in finance and insurance.
About the Author
Ludger Rüschendorf, Professor of Mathematical Stochastics, studied Mathematics, Physics and Economics in Münster. Diploma thesis 1972 - PhD 1974 in Hamburg in Asymptotic Statistics - Habilitation thesis 1979 in Aachen in the area of stochastic ordering, masstransportation and Fréchet bounds - Professorships in Germany: 1981-1987 in Freiburg, 1987-1993 in Münster, 1993- in Freiburg.
Table of Contents
Preface.-Part I: Stochastic Dependence and Extremal Risk.-1 Copulas, Sklar's Theorem, and Distributional Transform.- 2 Fréchet Classes, Risk Bounds, and Duality Theory.- 3 Convex Order, Excess of Loss, and Comonotonicity.- 4 Bounds for the Distribution Function and Value at Risk of the Joint Portfolio.- 5 Restrictions on the Dependence Structure.- 6 Dependence Orderings of Risk Vectors and Portfolios.- Part II: Risk Measures and Worst Case Portfolios.- 7 Risk Measures for Real Risks.- 8 Risk Measures for Portfolio Vectors.- 9 Law Invariant Convex Risk Measures on L_d^p and Optimal Mass Transportation.- Part III: Optimal Risk Allocation.- 10 Optimal Allocations and Pareto Equilibrium.- 11 Characterization and Examples of Optimal Risk Allocations for Convex Risk Functionals.- 12 Optimal Contingent Claims and (Re)Insurance Contracts.- Part IV: Optimal Portfolios and Extreme Risks.- 13 Optimal Portfolio Diversification w.r.t. Extreme Risks.- 14 Ordering of Multivariate Risk Models with Respect to Extreme Portfolio Losses.- References.- List of Symbols.- Index.