## Mathematics for Finance

An Introduction to Financial Engineering

Author: Marek Capinski,Tomasz Zastawniak

Publisher: Springer

ISBN: 1852338466

Page: 314

View: 3194

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 for Finance

An Introduction to Financial Engineering

Author: Marek Capinski,Tomasz Zastawniak

Publisher: Springer

ISBN: 9781447139782

Page: 314

View: 5986

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 for Finance

An Introduction to Financial Engineering

Author: Marek Capiński,Tomasz Zastawniak

Publisher: Springer

ISBN: 9780857290830

Category: Mathematics

Page: 336

View: 5511

As with the first edition, Mathematics for Finance: An Introduction to Financial Engineering combines financial motivation with mathematical style. Assuming only basic knowledge of probability and calculus, it presents three major areas of mathematical finance, namely Option pricing based on the no-arbitrage principle in discrete and continuous time setting, Markowitz portfolio optimisation and Capital Asset Pricing Model, and basic stochastic interest rate models in discrete setting. From the reviews of the first edition: ”This text is an excellent introduction to Mathematical Finance. Armed with a knowledge of basic calculus and probability a student can use this book to learn about derivatives, interest rates and their term structure and portfolio management.”(Zentralblatt MATH) ”Given these basic tools, it is surprising how high a level of sophistication the authors achieve, covering such topics as arbitrage-free valuation, binomial trees, and risk-neutral valuation.” (www.riskbook.com) ”The reviewer can only congratulate the authors with successful completion of a difficult task of writing a useful textbook on a traditionally hard topic.” (K. Borovkov, The Australian Mathematical Society Gazette, Vol. 31 (4), 2004)

## Measure, Integral and Probability

Author: Marek Capinski,(Peter) Ekkehard Kopp

Publisher: Springer Science & Business Media

ISBN: 1447136314

Category: Mathematics

Page: 227

View: 8340

This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

## The Mathematics of Finance

Modeling and Hedging

Author: Victor Goodman,Joseph Gail Stampfli

Publisher: American Mathematical Soc.

ISBN: 9780821847930

Page: 250

View: 1789

This book is ideally suited for an introductory undergraduate course on financial engineering. It explains the basic concepts of financial derivatives, including put and call options, as well as more complex derivatives such as barrier options and options on futures contracts. Both discrete and continuous models of market behavior are developed in this book. In particular, the analysis of option prices developed by Black and Scholes is explained in a self-contained way, using both the probabilistic Brownian Motion method and the analytical differential equations method. 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. In addition to theoretical results, numerical models are presented in much detail. Each of the eleven chapters includes a variety of exercises.

## An Introduction to Mathematical Finance with Applications

Understanding and Building Financial Intuition

Author: Arlie O. Petters,Xiaoying Dong

Publisher: Springer

ISBN: 1493937839

Category: Mathematics

Page: 483

View: 2673

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.

## Mathematical Finance

Theory, Modeling, Implementation

Author: Christian Fries

Publisher: John Wiley & Sons

ISBN: 9780470179772

Category: Mathematics

Page: 512

View: 7415

A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises. While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.

## Statistics and Data Analysis for Financial Engineering

with R examples

Author: David Ruppert,David S. Matteson

Publisher: Springer

ISBN: 1493926144

Page: 719

View: 1310

The new edition of this influential textbook, geared towards graduate or advanced undergraduate students, teaches the statistics necessary for financial engineering. In doing so, it illustrates concepts using financial markets and economic data, R Labs with real-data exercises, and graphical and analytic methods for modeling and diagnosing modeling errors. These methods are critical because financial engineers now have access to enormous quantities of data. To make use of this data, the powerful methods in this book for working with quantitative information, particularly about volatility and risks, are essential. Strengths of this fully-revised edition include major additions to the R code and the advanced topics covered. Individual chapters cover, among other topics, multivariate distributions, copulas, Bayesian computations, risk management, and cointegration. Suggested prerequisites are basic knowledge of statistics and probability, matrices and linear algebra, and calculus. There is an appendix on probability, statistics and linear algebra. Practicing financial engineers will also find this book of interest.

## An Introduction to the Mathematics of Finance

A Deterministic Approach

Author: Stephen Garrett

Publisher: Butterworth-Heinemann

ISBN: 0080982751

Category: Mathematics

Page: 464

View: 4708

An Introduction to the Mathematics of Finance: A Deterministic Approach, 2e, offers a highly illustrated introduction to mathematical finance, with a special emphasis on interest rates. This revision of the McCutcheon-Scott classic follows the core subjects covered by the first professional exam required of UK actuaries, the CT1 exam. It realigns the table of contents with the CT1 exam and includes sample questions from past exams of both The Actuarial Profession and the CFA Institute. With a wealth of solved problems and interesting applications, An Introduction to the Mathematics of Finance stands alone in its ability to address the needs of its primary target audience, the actuarial student. Closely follows the syllabus for the CT1 exam of The Institute and Faculty of Actuaries Features new content and more examples Online supplements available: http://booksite.elsevier.com/9780080982403/ Includes past exam questions from The Institute and Faculty of Actuaries and the CFA Institute

## An Introduction to Quantitative Finance

Author: Stephen Blyth

Publisher: Oxford University Press

ISBN: 0199666598

Page: 175

View: 7709

The quantitative nature of complex financial transactions makes them a fascinating subject area for mathematicians of all types. This book gives an insight into financial engineering while building on introductory probability courses by detailing one of the most fascinating applications of the subject.

## Discrete Models of Financial Markets

Author: Marek Capiński,Ekkehard Kopp

Publisher: Cambridge University Press

ISBN: 110700263X

Page: 192

View: 3289

An excellent basis for further study. Suitable even for readers with no mathematical background.

## An Elementary Introduction to Mathematical Finance

Author: Sheldon M. Ross

Publisher: Cambridge University Press

ISBN: 1139498037

Category: Mathematics

Page: N.A

View: 9718

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.

## Statistics and Finance

An Introduction

Author: David Ruppert

Publisher: Springer Science & Business Media

ISBN: 9780387202709

Page: 473

View: 9204

This textbook emphasizes the applications of statistics and probability to finance. It reviews the basics and advanced topics are introduced, including behavioral finance. The book serves as a text in courses, and those in the finance industry can use it for self-study.

## Elementary Probability Theory with Stochastic Processes

Author: K. L. Chung

Publisher: Springer Science & Business Media

ISBN: 1475751141

Category: Mathematics

Page: 325

View: 5193

In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.

## Introduction to the Mathematics of Finance

Author: Ruth J. Williams

Publisher: American Mathematical Soc.

ISBN: 0821839039

Page: 150

View: 4769

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 the discrete (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 a continuous market model that generalizes the simple Black-Scholes model in several directions.

## Basic Stochastic Processes

A Course Through Exercises

Author: Zdzislaw Brzezniak,Tomasz Zastawniak

Publisher: Springer Science & Business Media

ISBN: 1447105338

Category: Mathematics

Page: 226

View: 4766

Stochastic processes are tools used widely by statisticians and researchers working in the mathematics of finance. This book for self-study provides a detailed treatment of conditional expectation and probability, a topic that in principle belongs to probability theory, but is essential as a tool for stochastic processes. The book centers on exercises as the main means of explanation.

## Risk and Portfolio Analysis

Principles and Methods

Author: Henrik Hult,Filip Lindskog,Ola Hammarlid,Carl Johan Rehn

Publisher: Springer Science & Business Media

ISBN: 146144103X

Category: Mathematics

Page: 338

View: 4491

Investment and risk management problems are fundamental problems for financial institutions and involve both speculative and hedging decisions. A structured approach to these problems naturally leads one to the field of applied mathematics in order to translate subjective probability beliefs and attitudes towards risk and reward into actual decisions. In Risk and Portfolio Analysis the authors present sound principles and useful methods for making investment and risk management decisions in the presence of hedgeable and non-hedgeable risks using the simplest possible principles, methods, and models that still capture the essential features of the real-world problems. They use rigorous, yet elementary mathematics, avoiding technically advanced approaches which have no clear methodological purpose and are practically irrelevant. The material progresses systematically and topics such as the pricing and hedging of derivative contracts, investment and hedging principles from portfolio theory, and risk measurement and multivariate models from risk management are covered appropriately. The theory is combined with numerous real-world examples that illustrate how the principles, methods, and models can be combined to approach concrete problems and to draw useful conclusions. Exercises are included at the end of the chapters to help reinforce the text and provide insight. This book will serve advanced undergraduate and graduate students, and practitioners in insurance, finance as well as regulators. Prerequisites include undergraduate level courses in linear algebra, analysis, statistics and probability.

## Introduction to the Mathematics of Finance

From Risk Management to Options Pricing

Author: Steven Roman

Publisher: Springer Science & Business Media

ISBN: 1441990054

Category: Mathematics

Page: 356

View: 2882

An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.

## Financial Calculus

An Introduction to Derivative Pricing

Author: Martin Baxter,Andrew Rennie

Publisher: Cambridge University Press

ISBN: 1139643274

Category: Mathematics

Page: N.A

View: 9635

The rewards and dangers of speculating in the modern financial markets have come to the fore in recent times with the collapse of banks and bankruptcies of public corporations as a direct result of ill-judged investment. At the same time, individuals are paid huge sums to use their mathematical skills to make well-judged investment decisions. Here now is the first rigorous and accessible account of the mathematics behind the pricing, construction and hedging of derivative securities. Key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model are described with mathematical precision in a style tailored for market practitioners. Starting from discrete-time hedging on binary trees, continuous-time stock models (including Black-Scholes) are developed. Practicalities are stressed, including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. A full glossary of probabilistic and financial terms is provided. This unique book will be an essential purchase for market practitioners, quantitative analysts, and derivatives traders.

## Introduction to the Economics and Mathematics of Financial Markets

Author: Jakša Cvitanić,Fernando Zapatero

Publisher: MIT Press

ISBN: 9780262033206