Introductory Course On Financial Mathematics

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Introductory Course on Financial Mathematics

M V Tretyakov
Introductory Course on Financial Mathematics Book PDF

Author : M V Tretyakov
Publisher : World Scientific Publishing Company
Page : 276 pages
File Size : 50,8 Mb
Release : 2013-07-23
Category : Mathematics
ISBN : 9781908977403

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Introductory Course on Financial Mathematics by M V Tretyakov Pdf

This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple, but widely used, financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to understand the concepts considered in this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective of quantifying and hedging risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas concerning derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a ‘sandwich’ structure: probability and stochastics are given in situ where mathematics can be readily illustrated by application to finance. The first part of the book introduces one of the main principles in finance — ‘no arbitrage pricing’. It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. The second part deals with pricing and hedging of European- and American-type options in the discrete-time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time discrete-space stochastic processes used in financial modelling are considered. The third part introduces the Wiener process, Ito integrals and stochastic differential equations, but its main focus is the famous Black–Scholes formula for pricing European options. Some guidance for further study within this exciting and rapidly changing field is given in the concluding chapter. There are approximately 100 exercises interspersed throughout the book, and solutions for most problems are provided in the appendices.

An Introduction to Mathematical Finance with Applications

Arlie O. Petters,Xiaoying Dong
An Introduction to Mathematical Finance with Applications Book PDF

Author : Arlie O. Petters,Xiaoying Dong
Publisher : Springer
Page : 483 pages
File Size : 50,5 Mb
Release : 2016-06-17
Category : Mathematics
ISBN : 9781493937837

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An Introduction to Mathematical Finance with Applications by Arlie O. Petters,Xiaoying Dong Pdf

This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire textbook is appropriate for a single year-long course on introductory mathematical finance. The self-contained design of the text allows for instructor flexibility in topics courses and those focusing on financial derivatives. Moreover, the text is useful for mathematicians, physicists, and engineers who want to learn finance via an approach that builds their financial intuition and is explicit about model building, as well as business school students who want a treatment of finance that is deeper but not overly theoretical.

Mathematics for Finance

Marek Capinski,Tomasz Zastawniak
Mathematics for Finance Book PDF

Author : Marek Capinski,Tomasz Zastawniak
Publisher : Springer
Page : 314 pages
File Size : 49,7 Mb
Release : 2006-04-18
Category : Business & Economics
ISBN : 9781852338466

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Mathematics for Finance by Marek Capinski,Tomasz Zastawniak Pdf

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.

An Undergraduate Introduction to Financial Mathematics

J. Robert Buchanan
An Undergraduate Introduction to Financial Mathematics Book PDF

Author : J. Robert Buchanan
Publisher : World Scientific
Page : 372 pages
File Size : 46,5 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812835352

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An Undergraduate Introduction to Financial Mathematics by J. Robert Buchanan Pdf

"This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three or four semester sequence of calculus courses. It introduces the theory of interest, random variables and probability, stochastic processes, arbitrage, option pricing, hedging, and portfolio optimization. The student progresses from knowing only elementary calculus to understanding the derivation and solution of the Black-Scholes partial differential equation and its solutions. This is one of the few books on the subject of financial mathematics which is accessible to undergraduates having only a thorough grounding in elementary calculus. It explains the subject matter without 'hand waving' arguments and includes numerous examples. Every chapter concludes with a set of exercises which test the chapter's concepts and fill in details of derivations." -- Publisher's description.

Introduction to Financial Mathematics

Donald R. Chambers,Qin Lu
Introduction to Financial Mathematics Book PDF

Author : Donald R. Chambers,Qin Lu
Publisher : CRC Press
Page : 581 pages
File Size : 44,9 Mb
Release : 2021-06-16
Category : Computers
ISBN : 9781000370126

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Introduction to Financial Mathematics by Donald R. Chambers,Qin Lu Pdf

This book’s primary objective is to educate aspiring finance professionals about mathematics and computation in the context of financial derivatives. The authors offer a balance of traditional coverage and technology to fill the void between highly mathematical books and broad finance books. The focus of this book is twofold: To partner mathematics with corresponding intuition rather than diving so deeply into the mathematics that the material is inaccessible to many readers. To build reader intuition, understanding and confidence through three types of computer applications that help the reader understand the mathematics of the models. Unlike many books on financial derivatives requiring stochastic calculus, this book presents the fundamental theories based on only undergraduate probability knowledge. A key feature of this book is its focus on applying models in three programming languages –R, Mathematica and EXCEL. Each of the three approaches offers unique advantages. The computer applications are carefully introduced and require little prior programming background. The financial derivative models that are included in this book are virtually identical to those covered in the top financial professional certificate programs in finance. The overlap of financial models between these programs and this book is broad and deep.

Computational Finance

Argimiro Arratia
Computational Finance Book PDF

Author : Argimiro Arratia
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 51,9 Mb
Release : 2014-05-08
Category : Computers
ISBN : 9789462390706

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Computational Finance by Argimiro Arratia Pdf

The book covers a wide range of topics, yet essential, in Computational Finance (CF), understood as a mix of Finance, Computational Statistics, and Mathematics of Finance. In that regard it is unique in its kind, for it touches upon the basic principles of all three main components of CF, with hands-on examples for programming models in R. Thus, the first chapter gives an introduction to the Principles of Corporate Finance: the markets of stock and options, valuation and economic theory, framed within Computation and Information Theory (e.g. the famous Efficient Market Hypothesis is stated in terms of computational complexity, a new perspective). Chapters 2 and 3 give the necessary tools of Statistics for analyzing financial time series, it also goes in depth into the concepts of correlation, causality and clustering. Chapters 4 and 5 review the most important discrete and continuous models for financial time series. Each model is provided with an example program in R. Chapter 6 covers the essentials of Technical Analysis (TA) and Fundamental Analysis. This chapter is suitable for people outside academics and into the world of financial investments, as a primer in the methods of charting and analysis of value for stocks, as it is done in the financial industry. Moreover, a mathematical foundation to the seemly ad-hoc methods of TA is given, and this is new in a presentation of TA. Chapter 7 reviews the most important heuristics for optimization: simulated annealing, genetic programming, and ant colonies (swarm intelligence) which is material to feed the computer savvy readers. Chapter 8 gives the basic principles of portfolio management, through the mean-variance model, and optimization under different constraints which is a topic of current research in computation, due to its complexity. One important aspect of this chapter is that it teaches how to use the powerful tools for portfolio analysis from the RMetrics R-package. Chapter 9 is a natural continuation of chapter 8 into the new area of research of online portfolio selection. The basic model of the universal portfolio of Cover and approximate methods to compute are also described.

A First Course in Quantitative Finance

Thomas Mazzoni
A First Course in Quantitative Finance Book PDF

Author : Thomas Mazzoni
Publisher : Cambridge University Press
Page : 599 pages
File Size : 55,9 Mb
Release : 2018-03-29
Category : Business & Economics
ISBN : 9781108419574

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A First Course in Quantitative Finance by Thomas Mazzoni Pdf

Using stereoscopic images and other novel pedagogical features, this book offers a comprehensive introduction to quantitative finance.

Mathematics of Finance

Donald G. Saari
Mathematics of Finance Book PDF

Author : Donald G. Saari
Publisher : Springer Nature
Page : 144 pages
File Size : 51,9 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9783030254438

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Mathematics of Finance by Donald G. Saari Pdf

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.

Introductory Mathematical Analysis for Quantitative Finance

Daniele Ritelli,Giulia Spaletta
Introductory Mathematical Analysis for Quantitative Finance Book PDF

Author : Daniele Ritelli,Giulia Spaletta
Publisher : CRC Press
Page : 322 pages
File Size : 47,8 Mb
Release : 2020-04-13
Category : Mathematics
ISBN : 9781351245104

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Introductory Mathematical Analysis for Quantitative Finance by Daniele Ritelli,Giulia Spaletta Pdf

Introductory Mathematical Analysis for Quantitative Finance is a textbook designed to enable students with little knowledge of mathematical analysis to fully engage with modern quantitative finance. A basic understanding of dimensional Calculus and Linear Algebra is assumed. The exposition of the topics is as concise as possible, since the chapters are intended to represent a preliminary contact with the mathematical concepts used in Quantitative Finance. The aim is that this book can be used as a basis for an intensive one-semester course. Features: Written with applications in mind, and maintaining mathematical rigor. Suitable for undergraduate or master's level students with an Economics or Management background. Complemented with various solved examples and exercises, to support the understanding of the subject.

Introduction to the Economics and Mathematics of Financial Markets

Jaksa Cvitanic,Fernando Zapatero
Introduction to the Economics and Mathematics of Financial Markets Book PDF

Author : Jaksa Cvitanic,Fernando Zapatero
Publisher : MIT Press
Page : 528 pages
File Size : 43,8 Mb
Release : 2004-02-27
Category : Business & Economics
ISBN : 0262033208

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Introduction to the Economics and Mathematics of Financial Markets by Jaksa Cvitanic,Fernando Zapatero Pdf

An innovative textbook for use in advanced undergraduate and graduate courses; accessible to students in financial mathematics, financial engineering and economics. Introduction to the Economics and Mathematics of Financial Markets fills the longstanding need for an accessible yet serious textbook treatment of financial economics. The book provides a rigorous overview of the subject, while its flexible presentation makes it suitable for use with different levels of undergraduate and graduate students. Each chapter presents mathematical models of financial problems at three different degrees of sophistication: single-period, multi-period, and continuous-time. The single-period and multi-period models require only basic calculus and an introductory probability/statistics course, while an advanced undergraduate course in probability is helpful in understanding the continuous-time models. In this way, the material is given complete coverage at different levels; the less advanced student can stop before the more sophisticated mathematics and still be able to grasp the general principles of financial economics. The book is divided into three parts. The first part provides an introduction to basic securities and financial market organization, the concept of interest rates, the main mathematical models, and quantitative ways to measure risks and rewards. The second part treats option pricing and hedging; here and throughout the book, the authors emphasize the Martingale or probabilistic approach. Finally, the third part examines equilibrium models—a subject often neglected by other texts in financial mathematics, but included here because of the qualitative insight it offers into the behavior of market participants and pricing.

Financial Mathematics

Giuseppe Campolieti,Roman N. Makarov
Financial Mathematics Book PDF

Author : Giuseppe Campolieti,Roman N. Makarov
Publisher : CRC Press
Page : 662 pages
File Size : 46,5 Mb
Release : 2022-12-21
Category : Business & Economics
ISBN : 9780429889097

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Financial Mathematics by Giuseppe Campolieti,Roman N. Makarov Pdf

The book has been tested and refined through years of classroom teaching experience. 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. This textbook provides complete coverage of continuous-time financial models that form the cornerstones of financial derivative pricing theory. Unlike similar texts in the field, this one presents multiple problem-solving approaches, linking related comprehensive techniques for pricing different types of financial derivatives. Key features: In-depth coverage of continuous-time theory and methodology Numerous, fully worked out examples and exercises in every chapter Mathematically rigorous and consistent, yet bridging various basic and more advanced concepts Judicious balance of financial theory and mathematical methods Guide to Material This revision contains: Almost 150 pages worth of new material in all chapters A appendix on probability theory An expanded set of solved problems and additional exercises Answers to all exercises This book is a comprehensive, self-contained, and unified treatment of the main theory and application of mathematical methods behind modern-day financial mathematics. The text complements Financial Mathematics: A Comprehensive Treatment in Discrete Time, by the same authors, also published by CRC Press.

An Introduction to Financial Mathematics

Hugo D. Junghenn
An Introduction to Financial Mathematics Book PDF

Author : Hugo D. Junghenn
Publisher : CRC Press
Page : 318 pages
File Size : 48,8 Mb
Release : 2019-03-14
Category : Business & Economics
ISBN : 9780429554490

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An Introduction to Financial Mathematics by Hugo D. Junghenn Pdf

Introduction to Financial Mathematics: Option Valuation, Second Edition is a well-rounded primer to the mathematics and models used in the valuation of financial derivatives. The book consists of fifteen chapters, the first ten of which develop option valuation techniques in discrete time, the last five describing the theory in continuous time. The first half of the textbook develops basic finance and probability. The author then treats the binomial model as the primary example of discrete-time option valuation. The final part of the textbook examines the Black-Scholes model. The book is written to provide a straightforward account of the principles of option pricing and examines these principles in detail using standard discrete and stochastic calculus models. Additionally, the second edition has new exercises and examples, and includes many tables and graphs generated by over 30 MS Excel VBA modules available on the author’s webpage https://home.gwu.edu/~hdj/.

Introduction to Stochastic Calculus with Applications

Fima C. Klebaner
Introduction to Stochastic Calculus with Applications Book PDF

Author : Fima C. Klebaner
Publisher : Imperial College Press
Page : 431 pages
File Size : 51,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945557

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Introduction to Stochastic Calculus with Applications by Fima C. Klebaner Pdf

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

The Mathematics of Finance

Victor Goodman,Joseph Gail Stampfli
The Mathematics of Finance Book PDF

Author : Victor Goodman,Joseph Gail Stampfli
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 52,7 Mb
Release : 2009
Category : Capital market
ISBN : 9780821847930

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The Mathematics of Finance by Victor Goodman,Joseph Gail Stampfli Pdf

The book begins with binomial stock price models, moves on to multistage models, then to the Cox-Ross-Rubinstein option pricing process, and then to the Black-Scholes formula. Other topics presented include Zero Coupon Bonds, forward rates, the yield curve, and several bond price models. The book continues with foreign exchange models and the Keynes Interest Rate Parity Formula, and concludes with the study of country risk, a topic not inappropriate for the times."--pub. desc.

An Elementary Introduction to Mathematical Finance

Sheldon M. Ross
An Elementary Introduction to Mathematical Finance Book PDF

Author : Sheldon M. Ross
Publisher : Cambridge University Press
Page : 323 pages
File Size : 43,5 Mb
Release : 2011-02-28
Category : Mathematics
ISBN : 9781139498036

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An Elementary Introduction to Mathematical Finance by Sheldon M. Ross Pdf

This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.