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Non-Life Insurance Mathematics
"Offers a mathematical introduction to non-life insurance and, at the same time, to a multitude of applied stochastic processes. It gives detailed discussions of the fundamental models for claim sizes, claim arrivals, the total claim amount, and their probabilistic properties....The reader gets to know how the underlying probabilistic structures allow one to determine premiums in a portfolio or in an individual policy." --Zentralblatt für Didaktik der Mathematik
Introduction to Stochastic Programming
The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. At the same time, it is now being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal i...
Extreme Values, Regular Variation and Point Processes
This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.
Cooperative Stochastic Differential Games
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
Fundamentals of Convex Analysis and Optimization
This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, an...
Extreme Value Theory
Focuses on theoretical results along with applications All the main topics covering the heart of the subject are introduced to the reader in a systematic fashion Concentration is on the probabilistic and statistical aspects of extreme values Excellent introduction to extreme value theory at the graduate level, requiring only some mathematical maturity
Production Planning by Mixed Integer Programming
This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an int...
Analysis and Algorithms for Service Parts Supply Chains
* Provides a broad overview of modeling approaches and solution methodologies for addressing inventory problems, particularly the management of high cost, low demand rate service parts found in multi-echelon settings * The text may be used in a variety of courses for first-year graduate students or senior undergraduates, or as a reference for researchers and practitioners * A background in stochastic processes and optimization is assumed
