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Principles Of Infinitesimal Stochastic And Financial Analysis
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Book Synopsis Principles of Infinitesimal Stochastic and Financial Analysis by : Imme van den Berg
Download or read book Principles of Infinitesimal Stochastic and Financial Analysis written by Imme van den Berg and published by World Scientific. This book was released on 2000 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a tremendous growth in the volume of financial transactions based on mathematics, reflecting the confidence in the Nobel-Prize-winning Black-Scholes option theory. Risks emanating from obligatory future payments are covered by a strategy of trading with amounts not determined by guessing, but by solving equations, and with prices not resulting from offer and demand, but from computation. However, the mathematical theory behind that suffers from inaccessibility. This is due to the complexity of the mathematical foundation of the Black-Scholes model, which is the theory of continuous-time stochastic processes: a thorough study of mathematical finance is considered to be possible only at postgraduate level. The setting of this book is the discrete-time version of the Black-Scholes model, namely the Cox-Ross-Rubinstein model. The book gives a complete description of its background, which is now only the theory of finite stochastic processes. The novelty lies in the fact that orders of magnitude -- in the sense of nonstandard analysis -- are imposed on the parameters of the model. This not only makes the model more economically sound (such as rapid fluctuations of the market being represented by infinitesimal trading periods), but also leads to a significant simplification: the fundamental results of Black-Scholes theory are derived in full generality and with mathematical rigour, now at graduate level. The material has been repeatedly taught in a third-year course to econometricians.
Book Synopsis Principles Of Infinitesinal Stochastic & Financial Analysis by : Imme Van Den Berg
Download or read book Principles Of Infinitesinal Stochastic & Financial Analysis written by Imme Van Den Berg and published by World Scientific. This book was released on 2000-07-27 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been a tremendous growth in the volume of financial transactions based on mathematics, reflecting the confidence in the Nobel-Prize-winning Black-Scholes option theory. Risks emanating from obligatory future payments are covered by a strategy of trading with amounts not determined by guessing, but by solving equations, and with prices not resulting from offer and demand, but from computation. However, the mathematical theory behind that suffers from inaccessibility. This is due to the complexity of the mathematical foundation of the Black-Scholes model, which is the theory of continuous-time stochastic processes: a thorough study of mathematical finance is considered to be possible only at postgraduate level.The setting of this book is the discrete-time version of the Black-Scholes model, namely the Cox-Ross-Rubinstein model. The book gives a complete description of its background, which is now only the theory of finite stochastic processes. The novelty lies in the fact that orders of magnitude — in the sense of nonstandard analysis — are imposed on the parameters of the model. This not only makes the model more economically sound (such as rapid fluctuations of the market being represented by infinitesimal trading periods), but also leads to a significant simplification: the fundamental results of Black-Scholes theory are derived in full generality and with mathematical rigour, now at graduate level. The material has been repeatedly taught in a third-year course to econometricians.
Book Synopsis Principles of Infinitesimal Stochastic and Financial Analysis by : I. van den Berg
Download or read book Principles of Infinitesimal Stochastic and Financial Analysis written by I. van den Berg and published by . This book was released on 1996 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of Infinitesimal Stochastic Analysis by : K.D. Stroyan
Download or read book Foundations of Infinitesimal Stochastic Analysis written by K.D. Stroyan and published by Elsevier. This book was released on 2011-08-18 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Book Synopsis Introductory Stochastic Analysis for Finance and Insurance by : X. Sheldon Lin
Download or read book Introductory Stochastic Analysis for Finance and Insurance written by X. Sheldon Lin and published by John Wiley & Sons. This book was released on 2006-04-21 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Incorporates the many tools needed for modeling and pricing infinance and insurance Introductory Stochastic Analysis for Finance and Insuranceintroduces readers to the topics needed to master and use basicstochastic analysis techniques for mathematical finance. The authorpresents the theories of stochastic processes and stochasticcalculus and provides the necessary tools for modeling and pricingin finance and insurance. Practical in focus, the book's emphasisis on application, intuition, and computation, rather thantheory. Consequently, the text is of interest to graduate students,researchers, and practitioners interested in these areas. While thetext is self-contained, an introductory course in probabilitytheory is beneficial to prospective readers. This book evolved from the author's experience as an instructor andhas been thoroughly classroom-tested. Following an introduction,the author sets forth the fundamental information and tools neededby researchers and practitioners working in the financial andinsurance industries: * Overview of Probability Theory * Discrete-Time stochastic processes * Continuous-time stochastic processes * Stochastic calculus: basic topics The final two chapters, Stochastic Calculus: Advanced Topics andApplications in Insurance, are devoted to more advanced topics.Readers learn the Feynman-Kac formula, the Girsanov's theorem, andcomplex barrier hitting times distributions. Finally, readersdiscover how stochastic analysis and principles are applied inpractice through two insurance examples: valuation of equity-linkedannuities under a stochastic interest rate environment andcalculation of reserves for universal life insurance. Throughout the text, figures and tables are used to help simplifycomplex theory and pro-cesses. An extensive bibliography opens upadditional avenues of research to specialized topics. Ideal for upper-level undergraduate and graduate students, thistext is recommended for one-semester courses in stochastic financeand calculus. It is also recommended as a study guide forprofessionals taking Causality Actuarial Society (CAS) and Societyof Actuaries (SOA) actuarial examinations.
Book Synopsis An Infinitesimal Approach to Stochastic Analysis by : H. Jerome Keisler
Download or read book An Infinitesimal Approach to Stochastic Analysis written by H. Jerome Keisler and published by American Mathematical Soc.. This book was released on 1984 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph uses Robinson's infinitesimal (i.e., nonstandard) analysis to study stochastic integral equations with respect to a Brownian motion. By using a combination of standard and infinitesimal methods, we obtain new results about stochastic integral equations which can be stated in standard terms.
Book Synopsis Handbook of Market Risk by : Christian Szylar
Download or read book Handbook of Market Risk written by Christian Szylar and published by John Wiley & Sons. This book was released on 2013-12-04 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ONE-STOP GUIDE FOR THE THEORIES, APPLICATIONS, AND STATISTICAL METHODOLOGIES OF MARKET RISK Understanding and investigating the impacts of market risk on the financial landscape is crucial in preventing crises. Written by a hedge fund specialist, the Handbook of Market Risk is the comprehensive guide to the subject of market risk. Featuring a format that is accessible and convenient, the handbook employs numerous examples to underscore the application of the material in a real-world setting. The book starts by introducing the various methods to measure market risk while continuing to emphasize stress testing, liquidity, and interest rate implications. Covering topics intrinsic to understanding and applying market risk, the handbook features: An introduction to financial markets The historical perspective from market events and diverse mathematics to the value-at-risk Return and volatility estimates Diversification, portfolio risk, and efficient frontier The Capital Asset Pricing Model and the Arbitrage Pricing Theory The use of a fundamental multi-factors model Financial derivatives instruments Fixed income and interest rate risk Liquidity risk Alternative investments Stress testing and back testing Banks and Basel II/III The Handbook of Market Risk is a must-have resource for financial engineers, quantitative analysts, regulators, risk managers in investments banks, and large-scale consultancy groups advising banks on internal systems. The handbook is also an excellent text for academics teaching postgraduate courses on financial methodology.
Book Synopsis Neutrices and External Numbers by : Bruno Dinis
Download or read book Neutrices and External Numbers written by Bruno Dinis and published by CRC Press. This book was released on 2019-07-03 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it describes the family of algebraic laws characterizing the practice of calculations with external numbers. Features Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system. Outlines complete algebraic rules for the neutrices and external numbers Conducts operational analysis of convergence and integration of functions known up to orders of magnitude Formalises a calculus of error propagation, covariant with algebraic operations Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox
Book Synopsis Nonlinearity, Chaos, and Complexity by : Cristoforo Sergio Bertuglia
Download or read book Nonlinearity, Chaos, and Complexity written by Cristoforo Sergio Bertuglia and published by OUP Oxford. This book was released on 2005-05-12 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a broad range of topics, this text provides a comprehensive survey of the modelling of chaotic dynamics and complexity in the natural and social sciences. Its attention to models in both the physical and social sciences and the detailed philosophical approach make this an unique text in the midst of many current books on chaos and complexity. Part 1 deals with the mathematical model as an instrument of investigation. The general meaning of modelling and, more specifically, questions concerning linear modelling are discussed. Part 2 deals with the theme of chaos and the origin of chaotic dynamics. Part 3 deals with the theme of complexity: a property of the systems and of their models which is intermediate between stability and chaos. Including an extensive index and bibliography along with numerous examples and simplified models, this is an ideal course text.
Book Synopsis Stochastic Calculus with Infinitesimals by : Frederik S. Herzberg
Download or read book Stochastic Calculus with Infinitesimals written by Frederik S. Herzberg and published by Springer. This book was released on 2012-11-06 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Book Synopsis Foundations of Infinitesimal Stochastic Analysis by : K. D. Stroyan
Download or read book Foundations of Infinitesimal Stochastic Analysis written by K. D. Stroyan and published by . This book was released on 1986 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Stochastic Processes by : Dmytro Gusak
Download or read book Theory of Stochastic Processes written by Dmytro Gusak and published by Springer Science & Business Media. This book was released on 2010-07-10 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the necessary materials within a theoretical framework, this volume presents stochastic principles and processes, and related areas. Over 1000 exercises illustrate the concepts discussed, including modern approaches to sample paths and optimal stopping.
Book Synopsis Stochastic Analysis, Stochastic Systems, and Applications to Finance by : Allanus Hak-Man Tsoi
Download or read book Stochastic Analysis, Stochastic Systems, and Applications to Finance written by Allanus Hak-Man Tsoi and published by World Scientific. This book was released on 2011 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin
Download or read book CMUC written by and published by . This book was released on 2017 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hypermodels In Mathematical Finance: Modelling Via Infinitesimal Analysis by : Siu-ah Ng
Download or read book Hypermodels In Mathematical Finance: Modelling Via Infinitesimal Analysis written by Siu-ah Ng and published by World Scientific. This book was released on 2003-01-23 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the beginning of the new millennium, two unstoppable processes are taking place in the world: (1) globalization of the economy; (2) information revolution. As a consequence, there is greater participation of the world population in capital market investment, such as bonds and stocks and their derivatives. Hence there is a need for risk management and analytic theory explaining the market. This leads to quantitative tools based on mathematical methods, i.e. the theory of mathematical finance.Ever since the pioneer work of Black, Scholes and Merton in the 70's, there has been rapid growth in the study of mathematical finance, involving ever more sophisticated mathematics. However, from the practitioner's point of view, it is desirable to have simpler and more useful mathematical tools.This book introduces research students and practitioners to the intuitive but rigorous hypermodel techniques in finance. It is based on Robinson's infinitesimal analysis, which is easily grasped by anyone with as little background as first-year calculus. It covers topics such as pricing derivative securities (including the Black-Scholes formula), hedging, term structure models of interest rates, consumption and equilibrium. The reader is introduced to mathematical tools needed for the aforementioned topics. Mathematical proofs and details are given in an appendix. Some programs in MATHEMATICA are also included.
Book Synopsis Stochastic Analysis and Applications to Finance by : Tusheng Zhang
Download or read book Stochastic Analysis and Applications to Finance written by Tusheng Zhang and published by World Scientific. This book was released on 2012 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. It covers the topics ranging from Markov processes, backward stochastic differential equations, stochastic partial differential equations, and stochastic control, to risk measure and risk theory.
Book Synopsis Deterministic And Stochastic Topics In Computational Finance by : Ovidiu Calin
Download or read book Deterministic And Stochastic Topics In Computational Finance written by Ovidiu Calin and published by World Scientific Publishing Company. This book was released on 2016-11-25 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: What distinguishes this book from other texts on mathematical finance is the use of both probabilistic and PDEs tools to price derivatives for both constant and stochastic volatility models, by which the reader has the advantage of computing explicitly a large number of prices for European, American and Asian derivatives.The book presents continuous time models for financial markets, starting from classical models such as Black-Scholes and evolving towards the most popular models today such as Heston and VAR.A key feature of the textbook is the large number of exercises, mostly solved, which are designed to help the reader to understand the material.The book is based on the author's lectures on topics on computational finance for senior and graduate students, delivered in USA (Princeton University and EMU), Taiwan and Kuwait. The prerequisites are an introductory course in stochastic calculus, as well as the usual calculus sequence.The book is addressed to undergraduate and graduate students in Masters of Finance programs as well as to those who wish to become more efficient in their practical applications.Topics covered:
