Aspects Of Mathematical Finance
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Mathematical Finance
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Author : Ernst Eberlein
language : en
Publisher: Springer Nature
Release Date : 2019-12-03
Mathematical Finance written by Ernst Eberlein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-03 with Mathematics categories.
Taking continuous-time stochastic processes allowing for jumps as its starting and focal point, this book provides an accessible introduction to the stochastic calculus and control of semimartingales and explains the basic concepts of Mathematical Finance such as arbitrage theory, hedging, valuation principles, portfolio choice, and term structure modelling. It bridges thegap between introductory texts and the advanced literature in the field. Most textbooks on the subject are limited to diffusion-type models which cannot easily account for sudden price movements. Such abrupt changes, however, can often be observed in real markets. At the same time, purely discontinuous processes lead to a much wider variety of flexible and tractable models. This explains why processes with jumps have become an established tool in the statistics and mathematics of finance. Graduate students, researchers as well as practitioners will benefit from this monograph.
Financial Statistics And Mathematical Finance
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Author : Ansgar Steland
language : en
Publisher: John Wiley & Sons
Release Date : 2012-06-21
Financial Statistics And Mathematical Finance written by Ansgar Steland and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-21 with Business & Economics categories.
Mathematical finance has grown into a huge area of research which requires a lot of care and a large number of sophisticated mathematical tools. Mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, it considers various aspects of the application of statistical methods in finance and illustrates some of the many ways that statistical tools are used in financial applications. Financial Statistics and Mathematical Finance: Provides an introduction to the basics of financial statistics and mathematical finance. Explains the use and importance of statistical methods in econometrics and financial engineering. Illustrates the importance of derivatives and calculus to aid understanding in methods and results. Looks at advanced topics such as martingale theory, stochastic processes and stochastic integration. Features examples throughout to illustrate applications in mathematical and statistical finance. Is supported by an accompanying website featuring R code and data sets. Financial Statistics and Mathematical Finance introduces the financial methodology and the relevant mathematical tools in a style that is both mathematically rigorous and yet accessible to advanced level practitioners and mathematicians alike, both graduate students and researchers in statistics, finance, econometrics and business administration will benefit from this book.
Aspects Of Mathematical Finance
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Author : Marc Yor
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-02-13
Aspects Of Mathematical Finance written by Marc Yor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-13 with Mathematics categories.
This collection of essays is based on lectures given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance. The collection develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes. The book also features a description of the trainings of French financial analysts.
Stochastic Calculus For Finance
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Author : Marek Capiński
language : en
Publisher: Cambridge University Press
Release Date : 2012-08-23
Stochastic Calculus For Finance written by Marek Capiński and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-23 with Business & Economics categories.
This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.
Advanced Modelling In Mathematical Finance
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Author : Jan Kallsen
language : en
Publisher: Springer
Release Date : 2016-12-01
Advanced Modelling In Mathematical Finance written by Jan Kallsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-01 with Mathematics categories.
This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.
Mathematics For Finance
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Author : Marek Capinski
language : en
Publisher: Springer
Release Date : 2006-04-18
Mathematics For Finance written by Marek Capinski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-18 with Business & Economics categories.
This textbook contains the fundamentals for an undergraduate course in mathematical finance aimed primarily at students of mathematics. Assuming only a basic knowledge of probability and calculus, the material is presented in a mathematically rigorous and complete way. The book covers the time value of money, including the time structure of interest rates, bonds and stock valuation; derivative securities (futures, options), modelling in discrete time, pricing and hedging, and many other core topics. With numerous examples, problems and exercises, this book is ideally suited for independent study.
Mathematics Of Finance
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Author : Donald G. Saari
language : en
Publisher: Springer Nature
Release Date : 2019-08-31
Mathematics Of Finance written by Donald G. Saari and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-31 with Mathematics categories.
This textbook invites the reader to develop a holistic grounding in mathematical finance, where concepts and intuition play as important a role as powerful mathematical tools. Financial interactions are characterized by a vast amount of data and uncertainty; navigating the inherent dangers and hidden opportunities requires a keen understanding of what techniques to apply and when. By exploring the conceptual foundations of options pricing, the author equips readers to choose their tools with a critical eye and adapt to emerging challenges. Introducing the basics of gambles through realistic scenarios, the text goes on to build the core financial techniques of Puts, Calls, hedging, and arbitrage. Chapters on modeling and probability lead into the centerpiece: the Black–Scholes equation. Omitting the mechanics of solving Black–Scholes itself, the presentation instead focuses on an in-depth analysis of its derivation and solutions. Advanced topics that follow include the Greeks, American options, and embellishments. Throughout, the author presents topics in an engaging conversational style. “Intuition breaks” frequently prompt students to set aside mathematical details and think critically about the relevance of tools in context. Mathematics of Finance is ideal for undergraduates from a variety of backgrounds, including mathematics, economics, statistics, data science, and computer science. Students should have experience with the standard calculus sequence, as well as a familiarity with differential equations and probability. No financial expertise is assumed of student or instructor; in fact, the text’s deep connection to mathematical ideas makes it suitable for a math capstone course. A complete set of the author’s lecture videos is available on YouTube, providing a comprehensive supplementary resource for a course or independent study.
Introduction To The Mathematics Of Finance
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Author : Ruth J. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Introduction To The Mathematics Of Finance written by Ruth J. Williams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Business & Economics categories.
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in thediscrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale,equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for acontinuous market model that generalizes the simple Black-Scholes model in several direct
Option Theory With Stochastic Analysis
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Author : Fred Espen Benth
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Option Theory With Stochastic Analysis written by Fred Espen Benth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
This is a very basic and accessible introduction to option pricing, invoking a minimum of stochastic analysis and requiring only basic mathematical skills. It covers the theory essential to the statistical modeling of stocks, pricing of derivatives with martingale theory, and computational finance including both finite-difference and Monte Carlo methods.
Machine Learning For Asset Managers
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Author : Marcos M. López de Prado
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-22
Machine Learning For Asset Managers written by Marcos M. López de Prado and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Business & Economics categories.
Successful investment strategies are specific implementations of general theories. An investment strategy that lacks a theoretical justification is likely to be false. Hence, an asset manager should concentrate her efforts on developing a theory rather than on backtesting potential trading rules. The purpose of this Element is to introduce machine learning (ML) tools that can help asset managers discover economic and financial theories. ML is not a black box, and it does not necessarily overfit. ML tools complement rather than replace the classical statistical methods. Some of ML's strengths include (1) a focus on out-of-sample predictability over variance adjudication; (2) the use of computational methods to avoid relying on (potentially unrealistic) assumptions; (3) the ability to "learn" complex specifications, including nonlinear, hierarchical, and noncontinuous interaction effects in a high-dimensional space; and (4) the ability to disentangle the variable search from the specification search, robust to multicollinearity and other substitution effects.