This is the seventh book in a set of ten published under the collective title of Foundations of Quantitative Finance. The targeted readers are students, researchers, and practitioners of quantitative finance who find that many sources for financial applications are written at a level assuming significant mathematical expertise.

The goal for this series is to provide a complete and detailed development of the many foundational mathematical theories and results one finds referenced in popular resources in finance and quantitative finance. The included topics have been curated from vast mathematics and finance literature for the express purpose of supporting applications in quantitative finance. The hope is that this series will advance the reader's career.

The series is logically sequential. Books I, III, and V develop foundational mathematical results needed for the probability theory and finance applications of Books II, IV, and VI, respectively. Books VII, VIII, and IX then develop results in the theory of stochastic processes, and Book X develops applications of these stochastic and other models to finance. All ten volumes are extensively self-referenced.

Book VII introduces and develops properties of Brownian motion, arguably the most famous of stochastic processes, as well as two other classes of stochastic processes with properties enjoyed by Brownian motion, namely, Markov processes and martingales. Brownian motion is the central idea needed for most continuous time models in finance, and indeed most applications of stochastic processes. For some with more experience, this book will be the place to start in the series, while others will find Books I-VI provide a needed foundation.

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

Book I. Measure Spaces and Measurable Functions

Book II. Probability Spaces and Random Variables

Book III. The Integrals of Riemann, 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 X. Classical Models and Applications in Finance

Autorentext

Robert R. Reitano is Professor of the Practice in Finance at the Brandeis International Business School where he specializes in risk management and quantitative finance, and where 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. He has taught as Visiting Professor at Wuhan University of Technology School of Economics, Reykjavik University School of Business, and as Adjunct Professor in Boston University's Masters Degree program in Mathematical Finance. Dr. Reitano consults in investment strategy and asset/liability risk management, was Chief Investment Officer of Controlled Risk Insurance Company (CRICO), 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 awarded biennially by the Investment Section of the Society of the Actuaries. Dr. Reitano has served as Vice-Chair of the Board of Directors of the Professional Risk Managers International Association (PRMIA) and on the Executive Committee of the PRMIA Board, and is currently a member of the PRMIA Boston Steering Committee, the Financial Research Committee of the Society of Actuaries, and other not-for-profit boards and investment committees.