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Monte Carlo Methods In Financial Engineering

Author: Paul Glasserman
Publisher: Springer Science & Business Media
ISBN: 0387216170
Size: 13.17 MB
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From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis

Affine Diffusions And Related Processes Simulation Theory And Applications

Author: Aurélien Alfonsi
Publisher: Springer
ISBN: 3319052217
Size: 68.72 MB
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This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error. It also presents some models, mostly in the field of finance, where these methods are relevant and provides some numerical experiments. The book explains the mathematical background to understand affine diffusions and analyze the accuracy of the schemes.

Pricing Derivatives Under L Vy Models

Author: Andrey Itkin
Publisher: Birkhäuser
ISBN: 1493967924
Size: 45.36 MB
Format: PDF
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This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

Monte Carlo And Quasi Monte Carlo Methods

Author: Ronald Cools
Publisher: Springer
ISBN: 3319335073
Size: 19.64 MB
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This book presents the refereed proceedings of the Eleventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Leuven (Belgium) in April 2014. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising, in particular, in finance, statistics and computer graphics.

Exotic Option Pricing And Advanced L Vy Models

Author: Andreas Kyprianou
Publisher: John Wiley & Sons
ISBN: 0470017201
Size: 25.20 MB
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Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward

Mathematik Und Technologie

Author: Christiane Rousseau
Publisher: Springer-Verlag
ISBN: 3642300928
Size: 21.80 MB
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Zusammen mit der Abstraktion ist die Mathematik das entscheidende Werkzeug für technologische Innovationen. Das Buch bietet eine Einführung in zahlreiche Anwendungen der Mathematik auf dem Gebiet der Technologie. Meist werden moderne Anwendungen dargestellt, die heute zum Alltag gehören. Die mathematischen Grundlagen für technologische Anwendungen sind dabei relativ elementar, was die Leistungsstärke der mathematischen Modellbildung und der mathematischen Hilfsmittel beweist. Mit zahlreichen originellen Übungen am Ende eines jeden Kapitels.

Monte Carlo Algorithmen

Author: Thomas Müller-Gronbach
Publisher: Springer-Verlag
ISBN: 3540891412
Size: 46.86 MB
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Der Text gibt eine Einführung in die Mathematik und die Anwendungsmöglichkeiten der Monte Carlo-Methoden und verwendet dazu durchgängig die Sprache der Stochastik. Der Leser lernt die Grundprinzipien und wesentlichen Eigenschaften dieser Verfahren kennen und wird dadurch in den Stand versetzt, dieses wichtige algorithmische Werkzeug kompetent einsetzen und die Ergebnisse interpretieren zu können. Anhand ausgewählter Fragestellungen wird er außerdem an aktuelle Forschungsfragen und -ergebnisse in diesem Bereich herangeführt. Behandelt werden die direkte Simulation, Methoden zur Simulation von Verteilungen und stochastischen Prozessen, Varianzreduktion, sowie Markov Chain Monte Carlo-Methoden und die hochdimensionale Integration. Es werden Anwendungsbeispiele aus der Teilchenphysik und der Finanz- und Versicherungsmathematik präsentiert, und anhand des Integrationsproblems wird gezeigt, wie sich die Frage nach optimalen Algorithmen formulieren und beantworten lässt.

Markov Chains

Author: Pierre Bremaud
Publisher: Springer Science & Business Media
ISBN: 9780387985091
Size: 71.64 MB
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Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.