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Focusing on the theory of mass transportation, this comprehensive two-volume work delves into the Monge-Kantorovich and Kantorovich-Rubinstein problems, exploring various solution approaches and their connections to functional analysis, probability theory, and mathematical economics. The second volume emphasizes practical applications in areas such as applied probability, queuing theory, and stochastic processes, making it a valuable resource for graduate students and researchers in theoretical and applied probability, operations research, and related fields.

Focusing on the optimal transfer of masses, this volume serves as a comprehensive reference for researchers in fields such as applied probability, operations research, computer science, and mathematical economics. It delves into mass transportation problems, providing essential insights and methodologies relevant to the discipline.

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 first part introduces basic probabilistic tools and methods of distributional analysis, and describes their use to the modeling of dependence and to the derivation of risk bounds in these models. In the second, part risk measures with a particular focus on those in the financial and insurance context are presented. The final parts are then devoted to applications relevant to optimal risk allocation, optimal portfolio problems as well as to the optimization of insurance contracts. Good knowledge of basic probability and statistics as well as of basic general mathematics is a prerequisite for comfortably reading and working with the present volume, which is intended for graduate students, practitioners and researchers and can serve as a reference resource for the main concepts and techniques.