The Interval Market Model In Mathematical Finance

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The Interval Market Model in Mathematical Finance

Pierre Bernhard,Jacob C. Engwerda,Berend Roorda,J.M. Schumacher,Vassili Kolokoltsov,Patrick Saint-Pierre,Jean-Pierre Aubin
The Interval Market Model in Mathematical Finance Book PDF

Author : Pierre Bernhard,Jacob C. Engwerda,Berend Roorda,J.M. Schumacher,Vassili Kolokoltsov,Patrick Saint-Pierre,Jean-Pierre Aubin
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 44,6 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9780817683887

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The Interval Market Model in Mathematical Finance by Pierre Bernhard,Jacob C. Engwerda,Berend Roorda,J.M. Schumacher,Vassili Kolokoltsov,Patrick Saint-Pierre,Jean-Pierre Aubin Pdf

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous theory), instead opting for models that allowed minimax approaches to complement or replace stochastic methods. Among the most fruitful models were those utilizing game-theoretic tools and the so-called interval market model. Over time, these models have slowly but steadily gained influence in the financial community, providing a useful alternative to classical methods. A self-contained monograph, The Interval Market Model in Mathematical Finance: Game-Theoretic Methods assembles some of the most important results, old and new, in this area of research. Written by seven of the most prominent pioneers of the interval market model and game-theoretic finance, the work provides a detailed account of several closely related modeling techniques for an array of problems in mathematical economics. The book is divided into five parts, which successively address topics including: · probability-free Black-Scholes theory; · fair-price interval of an option; · representation formulas and fast algorithms for option pricing; · rainbow options; · tychastic approach of mathematical finance based upon viability theory. This book provides a welcome addition to the literature, complementing myriad titles on the market that take a classical approach to mathematical finance. It is a worthwhile resource for researchers in applied mathematics and quantitative finance, and has also been written in a manner accessible to financially-inclined readers with a limited technical background.

Mathematics of Financial Markets

Robert J Elliott,P. Ekkehard Kopp
Mathematics of Financial Markets Book PDF

Author : Robert J Elliott,P. Ekkehard Kopp
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 50,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475771466

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Mathematics of Financial Markets by Robert J Elliott,P. Ekkehard Kopp Pdf

This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.

Mathematical Finance

Michael Kohlmann,Tang Shanjian
Mathematical Finance Book PDF

Author : Michael Kohlmann,Tang Shanjian
Publisher : Birkhäuser
Page : 373 pages
File Size : 42,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882910

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Mathematical Finance by Michael Kohlmann,Tang Shanjian Pdf

The year 2000 is the centenary year of the publication of Bachelier's thesis which - together with Harry Markovitz Ph. D. dissertation on portfolio selection in 1952 and Fischer Black's and Myron Scholes' solution of an option pricing problem in 1973 - is considered as the starting point of modern finance as a mathematical discipline. On this remarkable anniversary the workshop on mathematical finance held at the University of Konstanz brought together practitioners, economists and mathematicians to discuss the state of the art. Apart from contributions to the known discrete, Brownian, and Lvy process models, first attempts to describe a market in a reasonable way by a fractional Brownian motion model are presented, opening many new aspects for practitioners and new problems for mathematicians. As most dynamical financial problems are stochastic filtering or control problems many talks presented adaptations of control methods and techniques to the classical financial problems in portfolio selection irreversible investment risk sensitive asset allocation capital asset pricing hedging contingent claims option pricing interest rate theory. The contributions of practitioners link the theoretical results to the steadily increasing flow of real world problems from financial institutions into mathematical laboratories. The present volume reflects this exchange of theoretical and applied results, methods and techniques that made the workshop a fruitful contribution to the interdisciplinary work in mathematical finance.

Mathematical Finance

Nikolai Dokuchaev
Mathematical Finance Book PDF

Author : Nikolai Dokuchaev
Publisher : Routledge
Page : 197 pages
File Size : 48,7 Mb
Release : 2007-02
Category : Business & Economics
ISBN : 9781134121984

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Mathematical Finance by Nikolai Dokuchaev Pdf

Rigorous in style, yet easy to use, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of Stochastic Analysis and statistical finance covered in most degree courses.

The Concepts and Practice of Mathematical Finance

Mark Suresh Joshi
The Concepts and Practice of Mathematical Finance Book PDF

Author : Mark Suresh Joshi
Publisher : Cambridge University Press
Page : 496 pages
File Size : 50,6 Mb
Release : 2003-12-24
Category : Business & Economics
ISBN : 0521823552

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The Concepts and Practice of Mathematical Finance by Mark Suresh Joshi Pdf

For those starting out as practitioners of mathematical finance, this is an ideal introduction. It provides the reader with a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Uniquely, the book includes extensive discussion of the ideas behind the models, and is even-handed in examining various approaches to the subject. Thus each pricing problem is solved using several methods. Worked examples and exercises, with answers, are provided in plenty, and computer projects are given for many problems. The author brings to this book a blend of practical experience and rigorous mathematical background, and supplies here the working knowledge needed to become a good quantitative analyst.

Mathematical Finance

Emanuela Rosazza Gianin,Carlo Sgarra
Mathematical Finance Book PDF

Author : Emanuela Rosazza Gianin,Carlo Sgarra
Publisher : Springer Nature
Page : 310 pages
File Size : 45,9 Mb
Release : 2023-04-18
Category : Mathematics
ISBN : 9783031283789

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Mathematical Finance by Emanuela Rosazza Gianin,Carlo Sgarra Pdf

The book is conceived as a guide to solve exercises in Mathematical Finance and a complement to theoretical lectures. The potential audience consists of students in Applied Mathematics, Engineering and Economics, attending courses in Mathematical Finance. The most important subjects covered by this textbook are Pricing and Hedging of different classes of financial derivatives (European, American Exotic options, Fixed Income derivatives) in the most popular modeling frameworks, both in discrete and continuous time setting, like the Binomial and the Black-Scholes models. A Chapter on static portfolio optimization, one on pricing for more advanced models and one on Risk Measures complete the overview on the main issues presented in classical courses on Mathematical Finance. About one hundred exercises are proposed, and a large amount of them provides a detailed solution, while a few are left as an exercise to the reader. Every chapter includes a brief resume of the main theoretical results to apply. This textbook is the result of several years of teaching experience of both the authors.

Lectures on the Mathematics of Finance

Ioannis Karatzas
Lectures on the Mathematics of Finance Book PDF

Author : Ioannis Karatzas
Publisher : American Mathematical Soc.
Page : 166 pages
File Size : 45,9 Mb
Release : 2024-06-30
Category : Business & Economics
ISBN : 0821870092

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Lectures on the Mathematics of Finance by Ioannis Karatzas Pdf

In this text, the author discusses the main aspects of mathematical finance. These include, arbitrage, hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained markets, equilibrium, and transaction costs. The book outlines advances made possible during the last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented with current research, and open problems are suggested. This tutorial survey of the rapidly expanding field of mathematical finance is addressed primarily to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students' mathematical skills, but always in connection with interesting applied problems.

Quantitative Analysis In Financial Markets: Collected Papers Of The New York University Mathematical Finance Seminar (Vol Ii)

Marco Avellaneda
Quantitative Analysis In Financial Markets Collected Papers Of The New York University Mathematical Finance Seminar Vol Ii Book PDF

Author : Marco Avellaneda
Publisher : World Scientific
Page : 379 pages
File Size : 41,8 Mb
Release : 2001-01-10
Category : Business & Economics
ISBN : 9789814493567

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Quantitative Analysis In Financial Markets: Collected Papers Of The New York University Mathematical Finance Seminar (Vol Ii) by Marco Avellaneda Pdf

This book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.

The Concepts and Practice of Mathematical Finance

Mark Suresh Joshi
The Concepts and Practice of Mathematical Finance Book PDF

Author : Mark Suresh Joshi
Publisher : Unknown
Page : 539 pages
File Size : 42,8 Mb
Release : 2008
Category : Derivative securities
ISBN : OCLC:802295799

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The Concepts and Practice of Mathematical Finance by Mark Suresh Joshi Pdf

An ideal introduction for those starting out as practitioners of mathematical finance, this book provides a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g. Black-Scholes, stochastic volatility, jump-diffusion and variance gamma, are examined. Both the theory and the implementation of the industry-standard LIBOR market model are considered in detail. Each pricing problem is approached using multiple techniques including the well-known PDE and martingale approaches. This second edition contains many more worked examples and over 200 exercises with detailed solutions. Extensive appendices provide a guide to jargon, a recap of the elements of probability theory, and a collection of computer projects. The author brings to this book a blend of practical experience and rigorous mathematical background and supplies here the working knowledge needed to become a good quantitative analyst.

Financial Mathematics

Giuseppe Campolieti,Roman N. Makarov
Financial Mathematics Book PDF

Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Page : 829 pages
File Size : 47,8 Mb
Release : 2016-04-28
Category : Business & Economics
ISBN : 9781498785662

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Financial Mathematics by Giuseppe Campolieti,Roman N. Makarov Pdf

Versatile for Several Interrelated Courses at the Undergraduate and Graduate Levels Financial Mathematics: A Comprehensive Treatment provides a unified, self-contained account of the main theory and application of methods behind modern-day financial mathematics. Tested and refined through years of the authors’ teaching experiences, the book encompasses a breadth of topics, from introductory to more advanced ones. Accessible to undergraduate students in mathematics, finance, actuarial science, economics, and related quantitative areas, much of the text covers essential material for core curriculum courses on financial mathematics. Some of the more advanced topics, such as formal derivative pricing theory, stochastic calculus, Monte Carlo simulation, and numerical methods, can be used in courses at the graduate level. Researchers and practitioners in quantitative finance will also benefit from the combination of analytical and numerical methods for solving various derivative pricing problems. With an abundance of examples, problems, and fully worked out solutions, the text introduces the financial theory and relevant mathematical methods in a mathematically rigorous yet engaging way. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. The book provides complete coverage of both discrete- and continuous-time financial models that form the cornerstones of financial derivative pricing theory. It also presents a self-contained introduction to stochastic calculus and martingale theory, which are key fundamental elements in quantitative finance.

Financial Market Analysis and Behaviour

Emil Dinga,Camelia Oprean-Stan,Cristina-Roxana Tănăsescu,Vasile Brătian,Gabriela-Mariana Ionescu
Financial Market Analysis and Behaviour Book PDF

Author : Emil Dinga,Camelia Oprean-Stan,Cristina-Roxana Tănăsescu,Vasile Brătian,Gabriela-Mariana Ionescu
Publisher : Taylor & Francis
Page : 299 pages
File Size : 50,8 Mb
Release : 2022-07-06
Category : Business & Economics
ISBN : 9781000609691

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Financial Market Analysis and Behaviour by Emil Dinga,Camelia Oprean-Stan,Cristina-Roxana Tănăsescu,Vasile Brătian,Gabriela-Mariana Ionescu Pdf

This book addresses the functioning of financial markets, in particular the financial market model, and modelling. More specifically, the book provides a model of adaptive preference in the financial market, rather than the model of the adaptive financial market, which is mostly based on Popper's objective propensity for the singular, i.e., unrepeatable, event. As a result, the concept of preference, following Simon's theory of satisficing, is developed in a logical way with the goal of supplying a foundation for a robust theory of adaptive preference in financial market behavior. The book offers new insights into financial market logic, and psychology: 1) advocating for the priority of behavior over information - in opposition to traditional financial market theories; 2) constructing the processes of (co)evolution adaptive preference-financial market using the concept of fetal reaction norms - between financial market and adaptive preference; 3) presenting a new typology of information in the financial market, aimed at proving point (1) above, as well as edifying an explicative mechanism of the evolutionary nature and behavior of the (real) financial market; 4) presenting sufficient, and necessary, principles or assumptions for developing a theory of adaptive preference in the financial market; and 5) proposing a new interpretation of the pair genotype-phenotype in the financial market model. The book's distinguishing feature is its research method, which is mainly logically rather than historically or empirically based. As a result, the book is targeted at generating debate about the best and most scientifically beneficial method of approaching, analyzing, and modelling financial markets.

Stochastic Finance

Nicolas Privault
Stochastic Finance Book PDF

Author : Nicolas Privault
Publisher : CRC Press
Page : 438 pages
File Size : 49,6 Mb
Release : 2013-12-20
Category : Business & Economics
ISBN : 9781466594036

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Stochastic Finance by Nicolas Privault Pdf

Stochastic Finance: An Introduction with Market Examples presents an introduction to pricing and hedging in discrete and continuous time financial models without friction, emphasizing the complementarity of analytical and probabilistic methods. It demonstrates both the power and limitations of mathematical models in finance, covering the basics of

Market Risk Analysis, Quantitative Methods in Finance

Carol Alexander
Market Risk Analysis Quantitative Methods in Finance Book PDF

Author : Carol Alexander
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 55,9 Mb
Release : 2008-04-30
Category : Business & Economics
ISBN : 9780470771020

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Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander Pdf

Written by leading market risk academic, Professor Carol Alexander, Quantitative Methods in Finance forms part one of the Market Risk Analysis four volume set. Starting from the basics, this book helps readers to take the first step towards becoming a properly qualified financial risk manager and asset manager, roles that are currently in huge demand. Accessible to intelligent readers with a moderate understanding of mathematics at high school level or to anyone with a university degree in mathematics, physics or engineering, no prior knowledge of finance is necessary. Instead the emphasis is on understanding ideas rather than on mathematical rigour, meaning that this book offers a fast-track introduction to financial analysis for readers with some quantitative background, highlighting those areas of mathematics that are particularly relevant to solving problems in financial risk management and asset management. Unique to this book is a focus on both continuous and discrete time finance so that Quantitative Methods in Finance is not only about the application of mathematics to finance; it also explains, in very pedagogical terms, how the continuous time and discrete time finance disciplines meet, providing a comprehensive, highly accessible guide which will provide readers with the tools to start applying their knowledge immediately. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Principal component analysis of European equity indices; Calibration of Student t distribution by maximum likelihood; Orthogonal regression and estimation of equity factor models; Simulations of geometric Brownian motion, and of correlated Student t variables; Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula; Cubic spline fitting of yields curves and implied volatilities; Solution of Markowitz problem with no short sales and other constraints; Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.

Discrete Models of Financial Markets

Marek Capiński
Discrete Models of Financial Markets Book PDF

Author : Marek Capiński
Publisher : Unknown
Page : 181 pages
File Size : 55,5 Mb
Release : 2012
Category : Finance
ISBN : 1139229133

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Discrete Models of Financial Markets by Marek Capiński Pdf

"This book explains in simple settings the fundamental ideas of financial market modelling and derivative pricing, using the no-arbitrage principle. Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox-Ross-Rubinstein (CRR) binomial tree model. A simple approach to discrete interest rate models is included, which, though elementary, has some novel features. All proofs are written in a user-friendly manner, with each step carefully explained and following a natural flow of thought. In this way the student learns how to tackle new problems"--

More Mathematical Finance

Mark Suresh Joshi
More Mathematical Finance Book PDF

Author : Mark Suresh Joshi
Publisher : Unknown
Page : 484 pages
File Size : 52,5 Mb
Release : 2011
Category : Business & Economics
ISBN : 0987122800

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More Mathematical Finance by Mark Suresh Joshi Pdf

The long-awaited sequel to the "Concepts and Practice of Mathematical Finance" has now arrived. Taking up where the first volume left off, a range of topics is covered in depth. Extensive sections include portfolio credit derivatives, quasi-Monte Carlo, the calibration and implementation of the LIBOR market model, the acceleration of binomial trees, the Fourier transform in option pricing and much more. Throughout Mark Joshi brings his unique blend of theory, lucidity, practicality and experience to bear on issues relevant to the working quantitative analyst. "More Mathematical Finance" is Mark Joshi's fourth book. His previous books including "C++ Design Patterns and Derivatives Pricing" and "Quant Job Interview Questions and Answers" have proven to be indispensable for individuals seeking to become quantitative analysts. His new book continues this trend with a clear exposition of a range of models and techniques in the field of derivatives pricing. Each chapter is accompanied by a set of exercises. These are of a variety of types including simple proofs, complicated derivations and computer projects. Chapter 1. Optionality, convexity and volatility 1 Chapter 2. Where does the money go? 9 Chapter 3. The Bachelier model 23 Chapter 4. Deriving the Delta 29 Chapter 5. Volatility derivatives and model-free dynamic replication 33 Chapter 6. Credit derivatives 41 Chapter 7. The Monte Carlo pricing of portfolio credit derivatives 53 Chapter 8. Quasi-analytic methods for pricing portfolio credit derivatives 71 Chapter 9. Implied correlation for portfolio credit derivatives 81 Chapter 10. Alternate models for portfolio credit derivatives 93 Chapter 11. The non-commutativity of discretization 113 Chapter 12. What is a factor? 129 Chapter 13. Early exercise and Monte Carlo Simulation 151 Chapter 14. The Brownian bridge 175 Chapter 15. Quasi Monte Carlo Simulation 185 Chapter 16. Pricing continuous barrier options using a jump-diffusion model 207 Chapter 17. The Fourier-Laplace transform and option pricing 219 Chapter 18. The cos method 253 Chapter 19. What are market models? 265 Chapter 20. Discounting in market models 281 Chapter 21. Drifts again 293 Chapter 22. Adjoint and automatic Greeks 307 Chapter 23. Estimating correlation for the LIBOR market model 327 Chapter 24. Swap-rate market models 341 Chapter 25. Calibrating market models 363 Chapter 26. Cross-currency market models 389 Chapter 27. Mixture models 401 Chapter 28. The convergence of binomial trees 407 Chapter 29. Asymmetry in option pricing 433 Chapter 30. A perfect model? 443 Chapter 31. The fundamental theorem of asset pricing. 449 Appendix A. The discrete Fourier transform 457 Praise for the Concepts and Practice of Mathematical Finance: "overshadows many other books available on the same subject" -- ZentralBlatt Math "Mark Joshi succeeds admirably - an excellent starting point for a numerate person in the field of mathematical finance." -- Risk Magazine "Very few books provide a balance between financial theory and practice. This book is one of the few books that strikes that balance." -- SIAM Review