Ludger Rüschendorf - Böcker

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.

This is the first comprehensive account of the theory of mass transportation problems and its applications. In volume I, the authors systematically develop the theory of mass transportation with emphasis to the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems, and their various extensions. They discuss a variety of different approaches towards solutions of these problems and exploit the rich interrelations to several mathematical sciences--from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications to the mass transportation and mass transshipment problems to topics in applied probability, theory of moments and distributions with given marginals, queucing theory, risk theory of probability metrics and its applications to various fields, amoung them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations, stochastic algorithms and rounding problems. The book will be useful to graduate students and researchers in the fields of theoretical and applied probabilitry, operations research, computer science, and mathematical economics.The prerequisites for this book are graduate level probability theory and real and functional analysis.

This is the first comprehensive account of the theory of mass transportation problems and its applications. In volume I, the authors systematically develop the theory of mass transportation with emphasis to the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems, and their various extensions. They discuss a variety of different approaches towards solutions of these problems and exploit the rich interrelations to several mathematical sciences--from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications to the mass transportation and mass transshipment problems to topics in applied probability, theory of moments and distributions with given marginals, queucing theory, risk theory of probability metrics and its applications to various fields, amoung them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations, stochastic algorithms and rounding problems. The book will be useful to graduate students and researchers in the fields of theoretical and applied probabilitry, operations research, computer science, and mathematical economics. The prerequisites for this book are graduate level probability theory and real and functional analysis.

The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.

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.

Eine gut motivierte Einführung in zentrale und vielfältige Themen, Methoden und Anwendungen der mathematischen Statistik wird in diesem Lehrbuch gegeben. Ausgehend von der statistischen Datenanalyse werden klassische und auch neuere Konstruktionsprinzipien für statistische Verfahren behandelt und begründet. Das Buch versucht neben den klassischen Themengebieten auch in neuere Anwendungen einzuführen. Diese reichen von Methoden der asymptotischen Statistik über nichtparametrische Schätzverfahren, robuste und sequentielle Tests sowie zur Statistik von Zählprozessen mit bedeutsamen Anwendungen z.B. in der Survival-Analyse bis hin zur Bildverarbeitung und Bildrekonstruktion und zum Quantile hedging in der Finanzmathematik.Das Buch zeigt, dass die Mathematische Statistik ein Gebiet mit vielen besonders schönen Ideen und Methoden und überraschenden Resultaten ist.

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.

Dieses Lehrbuch bietet eine umfassende, moderne Einführung in die wesentlichen Themen und Anwendungen der Wahrscheinlichkeitstheorie. Es liefert eine sehr gut motivierte, anspruchsvolle und weitreichende Darstellung, bleibt aber dennoch vorlesungsnah und verzichtet auf unnötige formalistische Hürden. Ziel des Autors ist es insbesondere, die Bedeutung und Faszination dieses Gebiets für zentrale Anwendungen spürbar werden zu lassen. Das Buch ermöglicht dem Leser somit, ein hervorragendes Verständnis der Begriffe, Methoden und der Kerninhalte der Wahrscheinlichkeitstheorie sowie der Grundlagen der stochastischen Prozesse und deren Anwendungen zu gewinnen.

Das Buch gibt eine Einführung in weiterführende Themengebiete der stochastischen Prozesse und der zugehörigen stochastischen Analysis und verbindet diese mit einer fundierten Darstellung von Grundlagen der Finanzmathematik. Es ist inhaltlich weitreichend und legt gleichzeitig viel Wert auf gute Lesbarkeit, Motivation und Erklärung der behandelten Sachverhalte. Finanzmathematische Fragestellungen werden zunächst im Rahmen diskreter Modelle eingeführt und dann auf zeitstetige Modelle übertragen. Die grundlegende Konstruktion des stochastischen Integrals und die zugehörige Martingaltheorie liefern fundamentale Methoden der Theorie stochastischer Prozesse zur Konstruktion von geeigneten stochastischen Modellen der Finanzmathematik, z.B. mit Hilfe von stochastischen Differentialgleichungen. Zentrale Resultate der stochastischen Analysis wie Itô -Formel, Satz von Girsanov und Martingaldarstellungssätze erhalten in der Finanzmathematik grundlegende Bedeutung, z.B. für die risiko-neutrale Bewertungsformel (Black-Scholes Formel) oder die Frage nach der Hedgebarkeit von Optionen und der Vollständigkeit von Marktmodellen. Kapitel zur Bewertung von Optionen in vollständigen und nichtvollständigen Märkten und zur Bestimmung optimaler Hedgingstrategien schließen die Thematik ab.Vorausgesetzt werden fortgeschrittene Kenntnisse der Wahrscheinlichkeitstheorie, insbesondere zu zeitdiskreten Prozessen (Martingale, Markov-Ketten) sowie zeitstetigen Prozessen (Brownsche Bewegung, Lévy-Prozesse, Prozesse mit unabhängigen Zuwächsen, Markovprozesse). Das Buch ist somit für fortgeschrittene Studierende als begleitende Lektüre sowie für Dozenten als Grundlage für eigene Lehrveranstaltungen geeignet.

The book provides an introduction to advanced topics in stochastic processes and related stochastic analysis, and combines them with a sound presentation of the fundamentals of financial mathematics.