Ludger Rüschendorf 
Mathematical Risk Analysis [PDF ebook] 
Dependence, Risk Bounds, Optimal Allocations and Portfolios

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. ​

Ludger Rüschendorf, Professor of Mathematical Stochastics, studied Mathematics, Physics and Economics in Münster. Diploma thesis 1972 – Ph D 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. He is elected member of the ISI, and author and co-author of several books and about 180 research papers.