Foundations of Quantitative Finance: III.  The Integrals of Riemann, Lebesgue and (Riemann-)Stieltjes  book cover
1st Edition

Foundations of Quantitative Finance: III. The Integrals of Riemann, Lebesgue and (Riemann-)Stieltjes

  • Available for pre-order on April 25, 2023. Item will ship after May 16, 2023
ISBN 9781032206547
May 16, 2023 Forthcoming by Chapman & Hall
290 Pages

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USD $89.95

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Book Description

Every financial professional wants and needs an advantage. A firm foundation in advanced mathematics can translate into dramatic advantages to professionals willing to obtain it. Many are not—and that is the advantage these books offer the astute reader.

Published under the collective title of Foundations of Quantitative Finance, this set of ten books presents the advanced mathematics finance professionals need to advance their careers. These books develop the theory most do not learn in Graduate Finance programs, or in most Financial Mathematics undergraduate and graduate courses.

As a high-level industry executive and authoritative instructor, Robert R. Reitano presents the mathematical theories he encountered and used in nearly three decades in the financial industry and two decades in education where he taught in highly respected graduate programs.

Readers should be quantitatively literate and familiar with the developments in the first books in the set. The set offers a linear progression through these topics, though each title can be studied independently since the collection is extensively self-referenced.

Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes, develops several approaches to an integration theory. The first two approaches were introduced in the Chapter 1 of Book I to motivate measure theory. The general theory of integration on measure spaces will be developed in Book V, and stochastic integrals then studies on Book VIII.

Book III Features:

  • Extensively referenced to utilize materials from earlier books.
  • Presents the theory needed to better understand applications.
  • Supplements previous training in mathematics, with more detailed developments.
  • Built from the author's five decades of experience in industry, research, and teaching.

Published and forthcoming titles in the Robert Reitano Quantitative Finance Series:

Book I: Measure Spaces and Measurable Functions.

Book II: Probability Spaces and Random Variables,

Book III: The Integrals of Lebesgue and (Riemann-) Stieltjes

Book IV: Distribution Functions and Expectations

Book V: General Measure and Integration Theory

Book VI: Densities, Transformed Distributions, and Limit Theorems

Book VII: Brownian Motion and Other Stochastic Processes

Book VIII: Itô Integration and Stochastic Calculus 1

Book IX: Stochastic Calculus 2 and Stochastic Differential Equations

Book 10: Applications and Classic Models

Table of Contents



  1. The Riemann Integral
  2. The Lebesgue Integral
  3. Lebesgue Integration and Differentiation
  4. Stieltjes Integration



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Robert R. Reitano is Professor of the Practice of Finance at the Brandeis International Business School where he specializes in risk management and quantitative finance. He previously served as MSF Program Director, and Senior Academic Director. He has a Ph.D. in Mathematics from MIT, is a Fellow of the Society of Actuaries, and a Chartered Enterprise Risk Analyst. Dr. Reitano consults in investment strategy and asset/liability risk management, and previously had a 29-year career at John Hancock/Manulife in investment strategy and asset/liability management, advancing to Executive Vice President & Chief Investment Strategist. His research papers have appeared in a number of journals and have won an Annual Prize of the Society of Actuaries and two F.M. Redington Prizes of the Investment Section of the Society of the Actuaries. Dr. Reitano serves on various not-for-profit boards and investment committees.