This textbook is for mathematicians and mathematical physicists and is mainly concerned with the physical justification of both the mathematical framework and the foundations of the theory of general relativity. Previous knowledge of the relevant physics is not assumed. This book is also suitable as an introduction to pseudo-Riemannian geometry with emphasis on geometrical concepts. A significant part of the text is devoted to the discussion of causality and singularity theorems. The insights obtained are applied to black hole astrophysics, thereby making the connection to current active research in mathematical physics and cosmology.

Value- and risk-oriented management is a holistic method of managing businesses. In this book both actuarial methods and methods pertaining to classical internal control and classical risk management are used. Therefore the approach taken is necessarily interdisciplinary. Indeed, there is a new dynamically developing field for actuaries as a result of the emphasis now on the measurement of risk.

This book provides the required basic knowledge for this subject from an actuarial perspective. It enables the reader to implement in practice a risk management system that is based on quantitative methods. With this book, the reader will additionally be able to critically appraise the applicability and the limits of the methods used in modern risk management.

"Value-oriented Management of Risk in Insurance" focuses on risk capital, capital allocation, performance measurement and value-oriented management. It also makes a connection to regulatory developments (for example, Solvency II). The reader should have a basic knowledge of probability and familiarity with mathematical concepts. It is intended for working actuaries and quantitative risk managers as well as actuarial students.

One of the most of exciting aspects is the general relativity pred- tion of black holes and the Such Big Bang. predictions gained weight the theorems through Penrose. singularity pioneered In various by te- books on theorems general relativity singularity are and then presented used to that black holes exist and that the argue universe started with a To date what has big been is bang. a critical of what lacking analysis these theorems predict-' We of really give a proof a typical singul- theorem and this ity use theorem to illustrate problems arising through the of possibilities violations" and "causality weak "shell very crossing These singularities." add to the problems weight of view that the point theorems alone singularity are not sufficient to the existence of predict physical singularities. The mathematical theme of the book In order to both solid gain a of and intuition understanding good for any mathematical theory, one, should to realise it as model of try a a fam- iar non-mathematical theories have had concept. Physical an especially the important on of and impact development mathematics, conversely various modern theories physical rather require sophisticated mathem- ics for their formulation. both and mathematics Today, physics are so that it is often difficult complex to master the theories in both very s- in the of jects. However, case differential pseudo-Riemannian geometry or the general relativity between and mathematics relationship physics is and it is therefore especially close, to from interd- possible profit an ciplinary approach.

Dieses Buch gibt einen methodisch fundierten Zugang zum wertorientierten Risikomanagement, einem fachubergreifenden Aufgabengebiet, das Komponenten aus dem Controlling und dem Aktuariat umfasst. Der anwendungsorientierten Ansatz versetzt den Leser in die Lage, ein auf quantitativen Methoden basiertes Risikomanagement unter kritischer Wurdigung seiner Grenzen praktisch im Unternehmen zu implementieren. Die Schwerpunkte des Buches sind hierbei Risikokapital und Kapitalallokation, Erfolgsmessung und wertorientierte Steuerung. Es wird ausserdem der Zusammenhang zu regulatorischen Entwicklungen (z. B. Solvency 2) hergestellt. In der Neuauflage wurden die Abschnitte uber Solvency 2 vollstandig uberarbeitet und aktualisiert. Ausserdem enthalt dieses Buch ausfuhrliche Rechenbeispiele, die in der Open Source Skriptensprache Julia programmiert wurden und aus dem Internet heruntergeladen werden koennen.