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Author: Svetlana Boyarchenko
Publisher: World Scientific
ISBN: 9814488615
Category : Business & Economics
Languages : en
Pages : 421
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Book Description
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Author: Svetlana Boyarchenko
Publisher: World Scientific
ISBN: 9814488615
Category : Business & Economics
Languages : en
Pages : 421
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Book Description
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Author: Francois Longin
Publisher: John Wiley & Sons
ISBN: 1118650336
Category : Business & Economics
Languages : en
Pages : 639
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Book Description
A guide to the growing importance of extreme value risk theory, methods, and applications in the financial sector Presenting a uniquely accessible guide, Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications features a combination of the theory, methods, and applications of extreme value theory (EVT) in finance and a practical understanding of market behavior including both ordinary and extraordinary conditions. Beginning with a fascinating history of EVTs and financial modeling, the handbook introduces the historical implications that resulted in the applications and then clearly examines the fundamental results of EVT in finance. After dealing with these theoretical results, the handbook focuses on the EVT methods critical for data analysis. Finally, the handbook features the practical applications and techniques and how these can be implemented in financial markets. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications includes: Over 40 contributions from international experts in the areas of finance, statistics, economics, business, insurance, and risk management Topical discussions on univariate and multivariate case extremes as well as regulation in financial markets Extensive references in order to provide readers with resources for further study Discussions on using R packages to compute the value of risk and related quantities The book is a valuable reference for practitioners in financial markets such as financial institutions, investment funds, and corporate treasuries, financial engineers, quantitative analysts, regulators, risk managers, large-scale consultancy groups, and insurers. Extreme Events in Finance: A Handbook of Extreme Value Theory and Its Applications is also a useful textbook for postgraduate courses on the methodology of EVTs in finance.
Author: Marco Corazza
Publisher: Springer Science & Business Media
ISBN: 8847014816
Category : Mathematics
Languages : en
Pages : 315
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Book Description
This book features selected papers from the international conference MAF 2008 that cover a wide variety of subjects in actuarial, insurance and financial fields, all treated in light of the successful cooperation between mathematics and statistics.
Author: Thorsten Rheinlander
Publisher: World Scientific
ISBN: 9814338796
Category : Business & Economics
Languages : en
Pages : 244
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Book Description
Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This volume provides a systematic treatment of hedging in incomplete markets. Mean-variance hedging under the risk-neutral measure is applied in the framework of exponential L vy processes and for derivatives written on defaultable assets. It is discussed how to complete markets based upon stochastic volatility models via trading in both stocks and vanilla options. Exponential utility indifference pricing is explored via a duality with entropy minimization. Backward stochastic differential equations offer an alternative approach and are moreover applied to study markets with trading constraints including basis risk. A range of optimal martingale measures are discussed including the entropy, Esscher and minimal martingale measures. Quasi-symmetry properties of stochastic processes are deployed in the semi-static hedging of barrier options. This book is directed towards both graduate students and researchers in mathematical finance, and will also provide an orientation to applied mathematicians, financial economists and practitioners wishing to explore recent progress in this field.
Author: Carlo Requião da Cunha
Publisher: CRC Press
ISBN: 1000464237
Category : Business & Economics
Languages : en
Pages : 332
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Book Description
Econophysics explores the parallels between physics and economics and is an exciting topic that is attracting increasing attention. However there is a lack of literature that explains the topic from a broad perspective. This book introduces advanced undergraduates and graduate students in physics and engineering to the topic from this outlook, and is accompanied by rigorous mathematics which ensures that this will also be a good guide for established researchers in the field as well as researchers from other fields, such as mathematics and statistics, who are interested in the topic. Key features: Presents a multidisciplinary approach that will be of interest to students and researchers from physics, engineering, mathematics, statistics, and other physical sciences Accompanied by Python code with further learning opportunities, available for readers to download from the CRC Press website. Accessible to both students and researchers Carlo R. da Cunha is an associate professor of physics and engineering physics at the Universidade Federal do Rio Grande do Sul (Brazil) and has been since 2011. Dr. da Cunha received his M.Sc. Degree from the West Virginia University in 2001 and his Ph.D. degree from Arizona State University in 2005. He was a postdoctoral researcher at McGill University in Canada in 2006 and an assistant professor of engineering at the University Federal de Santa Catarina between 2007 and 2011. He has been a guest professor at the Technische Universität Wien (Austria), Chiba University (Japan) and Arizona State University (US). His research revolves around the physics of complex systems where he has been drawing parallels between physical and economic systems from quantum to social levels. To access additional resources please take a lookhere.
Author: Andrea Pascucci
Publisher: Springer Science & Business Media
ISBN: 8847017815
Category : Mathematics
Languages : en
Pages : 727
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Book Description
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
Author: Alessandro Carbotti
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110664356
Category : Mathematics
Languages : en
Pages : 144
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Book Description
This book presents in a detailed and self-contained way a new and important density result in the analysis of fractional partial differential equations, while also covering several fundamental facts about space- and time-fractional equations.
Author: Michele Leonardo Bianchi
Publisher: World Scientific
ISBN: 9813276215
Category : Business & Economics
Languages : en
Pages : 598
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Book Description
The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
Author: Stefano M. Iacus
Publisher: Springer
ISBN: 3319555693
Category : Computers
Languages : en
Pages : 277
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Book Description
The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.
Author: José A. Tenreiro Machado
Publisher: MDPI
ISBN: 3906980472
Category : Science
Languages : en
Pages : 552
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Book Description
Printed Edition of the Special Issue Published in Entropy
