Das Buch bietet, begleitet von umfangreicher Analyse-Software, eine sehr gut verständliche Einführung in die Grundkonzepte der Finanzmathematik und des Financial Engineerings. Einen wesentlichen Bestandteil des Buchs bilden viele Fallbeispiele aus dem Bereich "Quantitative Finance" aus meiner konkreten Tätigkeit als Fonds-Manager, Gutachter und Berater im Bereich "Quantitative Finance". Das Buch soll Praktikern auf intuitiv sehr gut nachvollziehbare Weise die Grundtechniken der modernen Finanzmathematik nahebringen und es soll Finanzmathematikern die realen Anforderungen in der konkreten Anwendung finanzmathematischer Techniken in der Realität vermitteln. Für alle Leserschichten soll das Buch - trotz Vermittlung vieler Fakten - spannend und sehr gut lesbar sein und über die Vermittlung der Grundkompetenzen hinaus immer wieder neue Einsichten und überraschende Erkenntnisse bieten. Das Buch ist mit mathematischem Wissen auf Abitur-Niveau lesbar (Abschnitte für die tieferes mathematisches Wissen nötig ist, werden explizit gekennzeichnet).

This book is summarizing the results of the workshop "Uniform Distribution and Quasi-Monte Carlo Methods" of the RICAM Special Semester on "Applications of Algebra and Number Theory" in October 2013. The survey articles in this book focus on number theoretic point constructions, uniform distribution theory, and quasi-Monte Carlo methods. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules enjoy increasing popularity, with many fruitful applications in mathematical practice, as for example in finance, computer graphics, and biology. The goal of this book is to give an overview of recent developments in uniform distribution theory, quasi-Monte Carlo methods, and their applications, presented by leading experts in these vivid fields of research.

This volume is a collection of survey papers on recent developments in the fields of quasi-Monte Carlo methods and uniform random number generation. We will cover a broad spectrum of questions, from advanced metric number theory to pricing financial derivatives. The Monte Carlo method is one of the most important tools of system modeling. Deterministic algorithms, so-called uniform random number gen erators, are used to produce the input for the model systems on computers. Such generators are assessed by theoretical ("a priori") and by empirical tests. In the a priori analysis, we study figures of merit that measure the uniformity of certain high-dimensional "random" point sets. The degree of uniformity is strongly related to the degree of correlations within the random numbers. The quasi-Monte Carlo approach aims at improving the rate of conver gence in the Monte Carlo method by number-theoretic techniques. It yields deterministic bounds for the approximation error. The main mathematical tool here are so-called low-discrepancy sequences. These "quasi-random" points are produced by deterministic algorithms and should be as "super" uniformly distributed as possible. Hence, both in uniform random number generation and in quasi-Monte Carlo methods, we study the uniformity of deterministically generated point sets in high dimensions. By a (common) abuse oflanguage, one speaks of random and quasi-random point sets. The central questions treated in this book are (i) how to generate, (ii) how to analyze, and (iii) how to apply such high-dimensional point sets."

Monte Carlo methods are numerical methods based on random sampling and quasi-Monte Carlo methods are their deterministic versions. This volume contains the refereed proceedings of the Second International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the University of Salzburg (Austria) from July 9--12, 1996. The conference was a forum for recent progress in the theory and the applications of these methods. The topics covered in this volume range from theoretical issues in Monte Carlo and simulation methods, low-discrepancy point sets and sequences, lattice rules, and pseudorandom number generation to applications such as numerical integration, numerical linear algebra, integral equations, binary search, global optimization, computational physics, mathematical finance, and computer graphics. These proceedings will be of interest to graduate students and researchers in Monte Carlo and quasi-Monte Carlo methods, to numerical analysts, and to practitioners of simulation methods.

This textbook provides the necessary techniques from financial mathematics and stochastic analysis for the valuation of more complex financial products and strategies. The author discusses how to make use of mathematical methods to analyse volatilities in capital markets. Furthermore, he illustrates how to apply and extend the Black-Scholes theory to several fields in finance. In the final section of the book, the author introduces the readers to the fundamentals of stochastic analysis and presents examples of applications. This book builds on the previous volume of the author’s trilogy on quantitative finance. The aim of the second volume is to present and discuss more complex and advanced techniques of modern financial mathematics in a way that is intuitive and easy to follow. As in the previous volume, the author provides financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world.  

This textbook offers an easily understandable introduction to the fundamental concepts of financial mathematics and financial engineering. The author presents and discusses the basic concepts of financial engineering and illustrates how to trade and to analyze financial products with numerous examples. Special attention is given to the valuation of basic financial derivatives. In the final section of the book, the author introduces the Wiener Stock Price Model and the basic principles of Black-Scholes theory. The book’s aim is to introduce readers to the basic techniques of modern financial mathematics in a way that is intuitive and easy to follow, and to provide financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world. 

The textbook discusses risk management in capital markets and presents various techniques of portfolio optimization. Special attention is given to risk measurement and credit risk management. Furthermore, the author discusses optimal investment problems and presents various examples. In the last section, the book includes numerous case studies based on the author's own work as a fund manager, court-appointed expert and consultant in the field of quantitative finance. This book is the third volume of the quantitative finance trilogy by the author and builds on the theoretical groundwork introduced in the previous books. The volume presents real-life examples of the successful application of the introduced techniques and methods in financial services and capital markets.

Dieses Buch fuhrt auf allgemein verstandliche und spannende, aber auch (im besten Sinn) "belehrende" Weise in die Welt der Finanzderivate ein. In kompakter und anschaulicher Form prasentiert es ihren Handel, ihre Funktion, ihre Moeglichkeiten sowie die Rolle der Finanzmathematik und Spieltheorie in diesem Zusammenhang. Gerhard Larcher orientiert sich dabei an folgenden Fragestellungen: Wie gelangten Wirtschaftswissenschaftler wie Fisher Black, Myron Scholes und Robert Merton ausgehend von einfachen spieltheoretischen UEberlegungen (zum Beispiel zum Munzwurf) im Jahr 1972 schliesslich zur weltberuhmten Black-Scholes-Theorie, die die Finanzmarkte revolutionieren sollte, und fur die im Jahr 1997 an Scholes und Merton der Nobelpreis verliehen wurde? Kann man mit der Hilfe von Derivaten eine ganz konkrete, leicht durchfuhrbare Handelsstrategie entwerfen, mit deren Hilfe sich mit hoher Wahrscheinlichkeit uberdurchschnittliche Gewinne erzielen lassen?

Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.