Ralf Korn - Böcker

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath–Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models.The authors separately discuss Monte Carlo techniques, stochastic process basics, and the theoretical background and intuition behind financial and actuarial mathematics, before bringing the topics together to apply the Monte Carlo methods to areas of finance and insurance. This allows for the easy identification of standard Monte Carlo tools and for a detailed focus on the main principles of financial and insurance mathematics. The book describes high-level Monte Carlo methods for standard simulation and the simulation of stochastic processes with continuous and discontinuous paths. It also covers a wide selection of popular models in finance and insurance, from Black–Scholes to stochastic volatility to interest rate to dynamic mortality.Through its many numerical and graphical illustrations and simple, insightful examples, this book provides a deep understanding of the scope of Monte Carlo methods and their use in various financial situations. The intuitive presentation encourages readers to implement and further develop the simulation methods.

Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Romberg method, and the Heath–Platen estimator, as well as recent financial and actuarial models, such as the Cheyette and dynamic mortality models.The authors separately discuss Monte Carlo techniques, stochastic process basics, and the theoretical background and intuition behind financial and actuarial mathematics, before bringing the topics together to apply the Monte Carlo methods to areas of finance and insurance. This allows for the easy identification of standard Monte Carlo tools and for a detailed focus on the main principles of financial and insurance mathematics. The book describes high-level Monte Carlo methods for standard simulation and the simulation of stochastic processes with continuous and discontinuous paths. It also covers a wide selection of popular models in finance and insurance, from Black–Scholes to stochastic volatility to interest rate to dynamic mortality.Through its many numerical and graphical illustrations and simple, insightful examples, this book provides a deep understanding of the scope of Monte Carlo methods and their use in various financial situations. The intuitive presentation encourages readers to implement and further develop the simulation methods.

Das Lehrbuch gibt eine Einführung in typische Aufgabenstellungen der modernen Finanzmathematik. Dabei werden im einfachen zeitdiskreten Rahmen die wichtigsten finanzmathematischen Prinzipien (Arbitrage, Duplikation, Diversifikation) und Resultate (Fundamentalsätze der Optionsbewertung) vorgestellt, ohne dass bereits die Methoden der zeitstetigen Marktmodelle benötigt werden. Aufbauend auf der zeitstetigen Modellierung von Finanzmärkten werden dann die Probleme der Optionsbewertung (insbesondere die Black-Scholes-Formel) und der Portfolio-Optimierung (Optimale Investmentstrategien) behandelt. Die benötigten mathematischen Werkzeuge (wie Brownsche Bewegung, Martingaltheorie, Itô-Kalkül, stochastische Steuerung) werden in selbständigen Exkursen bereitgestellt.Direkte Beziehungen zur Anwendung in der Praxis der Finanzindustrie werden in einleitenden Abschnitten, durch die Vorstellung populärer Handels- und Garantiestrategien sowie zahlreicher numerischer Verfahren zur Bewertung exotischer Optionen hergestellt.Das Buch eignet sich als Grundlage einer Vorlesung, die sich an einen Grundkurs in Stochastik anschließt. Es richtet sich an Studierende der Mathematik und der Finanzwirtschaft sowie an Praktiker in Banken und Versicherungen.

Das vorliegende Buch und der zugehörige erste Band über Optionsbewertung und Portfolio-Optimierung geben eine gründliche Einführung in die Methoden und Prinzipien der modernen Finanzmathematik.

Dieses Buch beinhaltet fünf Dutzend Geschichten, die in lockerer, verständlicher und unterhaltsamer Form einen Einblick in die bunte Welt der Finanzmathematik und Finanzmärkte geben. Sie handeln von Renditen, Realzinssätzen, Barwerten, Arbitrage, Duplikation, Optionen, Swaps, der Black-Scholes-Gleichung und vielem mehr. Denken Sie mit, rechnen Sie mit und entdecken Sie, wie viele finanzmathematische Entscheidungen der Alltag Ihnen ständig abverlangt.  Die zweite Auflage wurde gegenüber der ersten deutlich erweitert, sowohl vom Umfang als auch von der thematischen Vielfalt her. Zahlreiche neue Geschichten entstammen den Gebieten Portfoliooptimierung und Versicherungsmathematik, stellen aber auch grundlegende Resultate und Methoden der Wahrscheinlichkeitstheorie vor. Ein Anhang gibt detaillierte Auskunft über die mathematischen Grundlagen.

This book follows a conversational approach in five dozen stories that provide an insight into the colorful world of financial mathematics and financial markets in a relaxed, accessible and entertaining form.

This book is devoted to Professor Jürgen Lehn, who passed away on September 29, 2008, at the age of 67. It contains invited papers that were presented at the Wo- shop on Recent Developments in Applied Probability and Statistics Dedicated to the Memory of Professor Jürgen Lehn, Middle East Technical University (METU), Ankara, April 23–24, 2009, which was jointly organized by the Technische Univ- sität Darmstadt (TUD) and METU. The papers present surveys on recent devel- ments in the area of applied probability and statistics. In addition, papers from the Panel Discussion: Impact of Mathematics in Science, Technology and Economics are included. Jürgen Lehn was born on the 28th of April, 1941 in Karlsruhe. From 1961 to 1968 he studied mathematics in Freiburg and Karlsruhe, and obtained a Diploma in Mathematics from the University of Karlsruhe in 1968. He obtained his Ph.D. at the University of Regensburg in 1972, and his Habilitation at the University of Karlsruhe in 1978. Later in 1978, he became a C3 level professor of Mathematical Statistics at the University of Marburg. In 1980 he was promoted to a C4 level professorship in mathematics at the TUD where he was a researcher until his death.

From 1961 to 1968 he studied mathematics in Freiburg and Karlsruhe, and obtained a Diploma in Mathematics from the University of Karlsruhe in 1968.