Discrete Time And Continuous Time Option Pricing With Fees

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Derivative Pricing in Discrete Time

Author : Nigel J. Cutland
Publisher : Springer Science & Business Media
ISBN 13 : 1447144082
Total Pages : 329 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Derivative Pricing in Discrete Time by : Nigel J. Cutland

Download or read book Derivative Pricing in Discrete Time written by Nigel J. Cutland and published by Springer Science & Business Media. This book was released on 2012-09-13 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the mathematical modelling of real world financial markets and the rational pricing of derivatives, which is part of the theory that not only underpins modern financial practice but is a thriving area of mathematical research. The central theme is the question of how to find a fair price for a derivative; defined to be a price at which it is not possible for any trader to make a risk free profit by trading in the derivative. To keep the mathematics as simple as possible, while explaining the basic principles, only discrete time models with a finite number of possible future scenarios are considered. The theory examines the simplest possible financial model having only one time step, where many of the fundamental ideas occur, and are easily understood. Proceeding slowly, the theory progresses to more realistic models with several stocks and multiple time steps, and includes a comprehensive treatment of incomplete models. The emphasis throughout is on clarity combined with full rigour. The later chapters deal with more advanced topics, including how the discrete time theory is related to the famous continuous time Black-Scholes theory, and a uniquely thorough treatment of American options. The book assumes no prior knowledge of financial markets, and the mathematical prerequisites are limited to elementary linear algebra and probability. This makes it accessible to undergraduates in mathematics as well as students of other disciplines with a mathematical component. It includes numerous worked examples and exercises, making it suitable for self-study.

Discrete-Time Approximations and Limit Theorems

Author : Yuliya Mishura
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110654245
Total Pages : 390 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Discrete-Time Approximations and Limit Theorems by : Yuliya Mishura

Download or read book Discrete-Time Approximations and Limit Theorems written by Yuliya Mishura and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-10-25 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

Option Pricing and Portfolio Optimization

Author : Ralf Korn
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821237
Total Pages : 272 pages
Book Rating : 4.8/5 (212 download)

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Book Synopsis Option Pricing and Portfolio Optimization by : Ralf Korn

Download or read book Option Pricing and Portfolio Optimization written by Ralf Korn and published by American Mathematical Soc.. This book was released on 2001 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills. The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended "excursions" from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes as applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.

Introduction to Option Pricing Theory

Author : Gopinath Kallianpur
Publisher : Springer Science & Business Media
ISBN 13 : 1461205115
Total Pages : 266 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Option Pricing Theory by : Gopinath Kallianpur

Download or read book Introduction to Option Pricing Theory written by Gopinath Kallianpur and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

American-Type Options

Author : Dmitrii S. Silvestrov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110389908
Total Pages : 672 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis American-Type Options by : Dmitrii S. Silvestrov

Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-03-03 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

A Behavioral Approach to Asset Pricing

Author : Hersh Shefrin
Publisher : Elsevier
ISBN 13 : 0080482244
Total Pages : 636 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis A Behavioral Approach to Asset Pricing by : Hersh Shefrin

Download or read book A Behavioral Approach to Asset Pricing written by Hersh Shefrin and published by Elsevier. This book was released on 2008-05-19 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: Behavioral finance is the study of how psychology affects financial decision making and financial markets. It is increasingly becoming the common way of understanding investor behavior and stock market activity. Incorporating the latest research and theory, Shefrin offers both a strong theory and efficient empirical tools that address derivatives, fixed income securities, mean-variance efficient portfolios, and the market portfolio. The book provides a series of examples to illustrate the theory. The second edition continues the tradition of the first edition by being the one and only book to focus completely on how behavioral finance principles affect asset pricing, now with its theory deepened and enriched by a plethora of research since the first edition

The Econometrics of Financial Markets

Author : John Y. Campbell
Publisher : Princeton University Press
ISBN 13 : 1400830214
Total Pages : 630 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Econometrics of Financial Markets by : John Y. Campbell

Download or read book The Econometrics of Financial Markets written by John Y. Campbell and published by Princeton University Press. This book was released on 2012-06-28 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past twenty years have seen an extraordinary growth in the use of quantitative methods in financial markets. Finance professionals now routinely use sophisticated statistical techniques in portfolio management, proprietary trading, risk management, financial consulting, and securities regulation. This graduate-level textbook is intended for PhD students, advanced MBA students, and industry professionals interested in the econometrics of financial modeling. The book covers the entire spectrum of empirical finance, including: the predictability of asset returns, tests of the Random Walk Hypothesis, the microstructure of securities markets, event analysis, the Capital Asset Pricing Model and the Arbitrage Pricing Theory, the term structure of interest rates, dynamic models of economic equilibrium, and nonlinear financial models such as ARCH, neural networks, statistical fractals, and chaos theory. Each chapter develops statistical techniques within the context of a particular financial application. This exciting new text contains a unique and accessible combination of theory and practice, bringing state-of-the-art statistical techniques to the forefront of financial applications. Each chapter also includes a discussion of recent empirical evidence, for example, the rejection of the Random Walk Hypothesis, as well as problems designed to help readers incorporate what they have read into their own applications.

Analysis of Financial Time Series

Author : Ruey S. Tsay
Publisher : John Wiley & Sons
ISBN 13 : 1118017099
Total Pages : 724 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Analysis of Financial Time Series by : Ruey S. Tsay

Download or read book Analysis of Financial Time Series written by Ruey S. Tsay and published by John Wiley & Sons. This book was released on 2010-10-26 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described. The author begins with basic characteristics of financial time series data before covering three main topics: Analysis and application of univariate financial time series The return series of multiple assets Bayesian inference in finance methods Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.

The Mathematics of Financial Modeling and Investment Management

Author : Sergio M. Focardi
Publisher : John Wiley & Sons
ISBN 13 : 0471674230
Total Pages : 802 pages
Book Rating : 4.4/5 (716 download)

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Book Synopsis The Mathematics of Financial Modeling and Investment Management by : Sergio M. Focardi

Download or read book The Mathematics of Financial Modeling and Investment Management written by Sergio M. Focardi and published by John Wiley & Sons. This book was released on 2004-04-12 with total page 802 pages. Available in PDF, EPUB and Kindle. Book excerpt: the mathematics of financial modeling & investment management The Mathematics of Financial Modeling & Investment Management covers a wide range of technical topics in mathematics and finance-enabling the investment management practitioner, researcher, or student to fully understand the process of financial decision-making and its economic foundations. This comprehensive resource will introduce you to key mathematical techniques-matrix algebra, calculus, ordinary differential equations, probability theory, stochastic calculus, time series analysis, optimization-as well as show you how these techniques are successfully implemented in the world of modern finance. Special emphasis is placed on the new mathematical tools that allow a deeper understanding of financial econometrics and financial economics. Recent advances in financial econometrics, such as tools for estimating and representing the tails of the distributions, the analysis of correlation phenomena, and dimensionality reduction through factor analysis and cointegration are discussed in depth. Using a wealth of real-world examples, Focardi and Fabozzi simultaneously show both the mathematical techniques and the areas in finance where these techniques are applied. They also cover a variety of useful financial applications, such as: * Arbitrage pricing * Interest rate modeling * Derivative pricing * Credit risk modeling * Equity and bond portfolio management * Risk management * And much more Filled with in-depth insight and expert advice, The Mathematics of Financial Modeling & Investment Management clearly ties together financial theory and mathematical techniques.

Optimization Techniques And Applications: International Conference (In 2 Volumes)

Author : F S Chou
Publisher : World Scientific
ISBN 13 : 9814554561
Total Pages : 1264 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Optimization Techniques And Applications: International Conference (In 2 Volumes) by : F S Chou

Download or read book Optimization Techniques And Applications: International Conference (In 2 Volumes) written by F S Chou and published by World Scientific. This book was released on 1992-05-25 with total page 1264 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the advent of powerful computers and novel mathematical programming techniques, the multidisciplinary field of optimization has advanced to the stage that quite complicated systems can be addressed. The conference was organized to provide a platform for the exchanging of new ideas and information and for identifying areas for future research. The contributions covered both theoretical techniques and a rich variety of case studies to which optimization can be usefully applied.

Numerical Methods in Finance and Economics

Author : Paolo Brandimarte
Publisher : John Wiley & Sons
ISBN 13 : 1118625579
Total Pages : 501 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Numerical Methods in Finance and Economics by : Paolo Brandimarte

Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.

Derivative Security Pricing

Author : Carl Chiarella
Publisher : Springer
ISBN 13 : 366245906X
Total Pages : 616 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Derivative Security Pricing by : Carl Chiarella

Download or read book Derivative Security Pricing written by Carl Chiarella and published by Springer. This book was released on 2015-03-25 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling. By focusing more on the financial intuition of the applications rather than the mathematical formalities, the book provides the essential knowledge and understanding of fundamental concepts of stochastic finance, and how to implement them to develop pricing models for derivatives as well as to model spot and forward interest rates. Furthermore an extensive overview of the associated literature is presented and its relevance and applicability are discussed. Most of the key concepts are covered including Ito’s Lemma, martingales, Girsanov’s theorem, Brownian motion, jump processes, stochastic volatility, American feature and binomial trees. The book is beneficial to higher-degree research students, academics and practitioners as it provides the elementary theoretical tools to apply the techniques of stochastic finance in research or industrial problems in the field.

Foundations of Reinforcement Learning with Applications in Finance

Author : Ashwin Rao
Publisher : CRC Press
ISBN 13 : 1000801055
Total Pages : 522 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Foundations of Reinforcement Learning with Applications in Finance by : Ashwin Rao

Download or read book Foundations of Reinforcement Learning with Applications in Finance written by Ashwin Rao and published by CRC Press. This book was released on 2022-12-16 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Reinforcement Learning with Applications in Finance aims to demystify Reinforcement Learning, and to make it a practically useful tool for those studying and working in applied areas — especially finance. Reinforcement Learning is emerging as a powerful technique for solving a variety of complex problems across industries that involve Sequential Optimal Decisioning under Uncertainty. Its penetration in high-profile problems like self-driving cars, robotics, and strategy games points to a future where Reinforcement Learning algorithms will have decisioning abilities far superior to humans. But when it comes getting educated in this area, there seems to be a reluctance to jump right in, because Reinforcement Learning appears to have acquired a reputation for being mysterious and technically challenging. This book strives to impart a lucid and insightful understanding of the topic by emphasizing the foundational mathematics and implementing models and algorithms in well-designed Python code, along with robust coverage of several financial trading problems that can be solved with Reinforcement Learning. This book has been created after years of iterative experimentation on the pedagogy of these topics while being taught to university students as well as industry practitioners. Features Focus on the foundational theory underpinning Reinforcement Learning and software design of the corresponding models and algorithms Suitable as a primary text for courses in Reinforcement Learning, but also as supplementary reading for applied/financial mathematics, programming, and other related courses Suitable for a professional audience of quantitative analysts or data scientists Blends theory/mathematics, programming/algorithms and real-world financial nuances while always striving to maintain simplicity and to build intuitive understanding To access the code base for this book, please go to: https://github.com/TikhonJelvis/RL-book.

Derivatives Markets

Author : David Goldenberg
Publisher : Routledge
ISBN 13 : 1317423550
Total Pages : 518 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Derivatives Markets by : David Goldenberg

Download or read book Derivatives Markets written by David Goldenberg and published by Routledge. This book was released on 2016-03-02 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Derivatives Markets is a thorough and well-presented textbook that offers readers an introduction to derivatives instruments, with a gentle introduction to mathematical finance, and provides a working knowledge of derivatives to a wide area of market participants. This new and accessible book provides a lucid, down-to-earth, theoretically rigorous but applied introduction to derivatives. Many insights have been discovered since the seminal work in the 1970s and the text provides a bridge to and incorporates them. It develops the skill sets needed to both understand and to intelligently use derivatives. These skill sets are developed in part by using concept checks that test the reader's understanding of the material as it is presented. The text discusses some fairly sophisticated topics not usually discussed in introductory derivatives texts. For example, real-world electronic market trading platforms such as CME’s Globex. On the theory side, a much needed and detailed discussion of what risk-neutral valuation really means in the context of the dynamics of the hedge portfolio. The text is a balanced, logical presentation of the major derivatives classes including forward and futures contracts in Part I, swaps in Part II, and options in Part III. The material is unified by providing a modern conceptual framework and exploiting the no-arbitrage relationships between the different derivatives classes. Some of the elements explained in detail in the text are: Hedging, Basis Risk, Spreading, and Spread Basis Risk Financial Futures Contracts, their Underlying Instruments, Hedging and Speculating OTC Markets and Swaps Option Strategies: Hedging and Speculating Risk-Neutral Valuation and the Binomial Option Pricing Model Equivalent Martingale Measures: The Modern Approach to Option Pricing Option Pricing in Continuous Time: from Bachelier to Black-Scholes and Beyond. Professor Goldenberg’s clear and concise explanations and end-of-chapter problems, guide the reader through the derivatives markets, developing the reader’s skill sets needed in order to incorporate and manage derivatives in a corporate or risk management setting. This textbook is for students, both undergraduate and postgraduate, as well as for those with an interest in how and why these markets work and thrive.

Financial Risk in Insurance

Author : G. Ottaviani
Publisher : Springer Science & Business Media
ISBN 13 : 3642578462
Total Pages : 123 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Financial Risk in Insurance by : G. Ottaviani

Download or read book Financial Risk in Insurance written by G. Ottaviani and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published with the contribution of the Italian insurance company, INA, this volume contains the invited contributions presented at the 3rd International AFIR Colloquium. In the spirit of actuarial tradition, the colloquium paid attention to the link between the theoretical approach and the operative problems of financial markets and institutions, and insurance companies in particular. The book is thus an important reference work for students and researchers of actuarial sciences and finance, and is also recommended to practitioners with theoretical interests.

The Oxford Guide to Financial Modeling

Author : Thomas S. Y. Ho
Publisher : Oxford University Press
ISBN 13 : 9780199727704
Total Pages : 770 pages
Book Rating : 4.7/5 (277 download)

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Book Synopsis The Oxford Guide to Financial Modeling by : Thomas S. Y. Ho

Download or read book The Oxford Guide to Financial Modeling written by Thomas S. Y. Ho and published by Oxford University Press. This book was released on 2004-01-15 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: The essential premise of this book is that theory and practice are equally important in describing financial modeling. In it the authors try to strike a balance in their discussions between theories that provide foundations for financial models and the institutional details that provide the context for applications of the models. The book presents the financial models of stock and bond options, exotic options, investment grade and high-yield bonds, convertible bonds, mortgage-backed securities, liabilities of financial institutions--the business model and the corporate model. It also describes the applications of the models to corporate finance. Furthermore, it relates the models to financial statements, risk management for an enterprise, and asset/liability management with illiquid instruments. The financial models are progressively presented from option pricing in the securities markets to firm valuation in corporate finance, following a format to emphasize the three aspects of a model: the set of assumptions, the model specification, and the model applications. Generally, financial modeling books segment the world of finance as "investments," "financial institutions," "corporate finance," and "securities analysis," and in so doing they rarely emphasize the relationships between the subjects. This unique book successfully ties the thought processes and applications of the financial models together and describes them as one process that provides business solutions. Created as a companion website to the book readers can visit www.thomasho.com to gain deeper understanding of the book's financial models. Interested readers can build and test the models described in the book using Excel, and they can submit their models to the site. Readers can also use the site's forum to discuss the models and can browse server based models to gain insights into the applications of the models. For those using the book in meetings or class settings the site provides Power Point descriptions of the chapters. Students can use available question banks on the chapters for studying.

Asymptotic Methods in Stochastics

Author : M. Csörgö
Publisher : American Mathematical Soc.
ISBN 13 : 0821835610
Total Pages : 546 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Asymptotic Methods in Stochastics by : M. Csörgö

Download or read book Asymptotic Methods in Stochastics written by M. Csörgö and published by American Mathematical Soc.. This book was released on 2004 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.