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This textbook provides complete coverage of discrete-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 discrete-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, mathematical, and computational methods. Guide to
Material. This revision contains: Almost 200 pages worth of new
material in all chapters. A new chapter on elementary probability
theory. An expanded the 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. Table of Contents List of Figures and Tables Preface I
Introduction to Pricing and Management of Financial Securities 1
Mathematics of Compounding 2 Primer on Pricing Risky Securities 3
Portfolio Management 4 Primer on Derivative Securities II
Discrete-Time Modelling 5 Single-Period Arrow–Debreu Models 6
Introduction to Discrete-Time Stochastic Calculus 7 Replication and
Pricing in the Binomial Tree Model 8 General Multi-Asset
Multi-Period Model Appendices A Elementary Probability Theory B
Glossary of Symbols and Abbreviations C Answers and Hints to
Exercises References Index Biographies Giuseppe Campolieti is
Professor of Mathematics at Wilfrid Laurier University in Waterloo,
Canada. He has been Natural Sciences and Engineering Research
Council postdoctoral research fellow and university research fellow
at the University of Toronto. In 1998, he joined the Masters in
Mathematical Finance as an instructor and later as an adjunct
professor in financial mathematics until 2002. Dr. Campolieti also
founded a financial software and consulting company in 1998. He
joined Laurier in 2002 as Associate Professor of Mathematics and as
SHARCNET Chair in Financial Mathematics. Roman N. Makarov is
Associate Professor and Chair of Mathematics at Wilfrid Laurier
University. Prior to joining Laurier in 2003, he was an Assistant
Professor of Mathematics at Siberian State University of
Telecommunications and Informatics and a senior research fellow at
the Laboratory of Monte Carlo Methods at the Institute of
Computational Mathematics and Mathematical Geophysics in
Novosibirsk, Russia.
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 discrete-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
discrete-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, mathematical, and
computational methods. Guide to Material. This revision contains:
Almost 200 pages worth of new material in all chapters. A new
chapter on elementary probability theory. An expanded the 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. Table of Contents List of Figures
and Tables Preface I Introduction to Pricing and Management of
Financial Securities 1 Mathematics of Compounding 2 Primer on
Pricing Risky Securities 3 Portfolio Management 4 Primer on
Derivative Securities II Discrete-Time Modelling 5 Single-Period
Arrow-Debreu Models 6 Introduction to Discrete-Time Stochastic
Calculus 7 Replication and Pricing in the Binomial Tree Model 8
General Multi-Asset Multi-Period Model Appendices A Elementary
Probability Theory B Glossary of Symbols and Abbreviations C
Answers and Hints to Exercises References Index Biographies
Giuseppe Campolieti is Professor of Mathematics at Wilfrid Laurier
University in Waterloo, Canada. He has been Natural Sciences and
Engineering Research Council postdoctoral research fellow and
university research fellow at the University of Toronto. In 1998,
he joined the Masters in Mathematical Finance as an instructor and
later as an adjunct professor in financial mathematics until 2002.
Dr. Campolieti also founded a financial software and consulting
company in 1998. He joined Laurier in 2002 as Associate Professor
of Mathematics and as SHARCNET Chair in Financial Mathematics.
Roman N. Makarov is Associate Professor and Chair of Mathematics at
Wilfrid Laurier University. Prior to joining Laurier in 2003, he
was an Assistant Professor of Mathematics at Siberian State
University of Telecommunications and Informatics and a senior
research fellow at the Laboratory of Monte Carlo Methods at the
Institute of Computational Mathematics and Mathematical Geophysics
in Novosibirsk, Russia.
In-depth coverage of discrete-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,
mathematical, and computational methods. Guide to Material.
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.
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