Mathematical Portfolio Theory and Analysis

Designed as a self-contained text, this book covers a wide spectrum of topics on portfolio theory. It covers both the classical-mean-variance portfolio theory as well as non-mean-variance portfolio theory. The book covers topics such as optimal portfolio strategies, bond portfolio optimization and risk management of portfolios. In order to ensure that the book is self-contained and not dependent on any pre-requisites, the book includes three chapters on basics of financial markets, probability theory and asset pricing models, which have resulted in a holistic narrative of the topic. Retaining the spirit of the classical works of stalwarts like Markowitz, Black, Sharpe, etc., this book includes various other aspects of portfolio theory, such as discrete and continuous time optimal portfolios, bond portfolios and risk management.

The increase in volume and diversity of banking activities has resulted in a concurrent enhanced importance of portfolio theory, both in terms of management perspective (including risk management) and the resulting mathematical sophistication required. Most books on portfolio theory are written either from the management perspective, or are aimed at advanced graduate students and academicians. This book bridges the gap between these two levels of learning. With many useful solved examples and exercises with solutions as well as a rigorous mathematical approach of portfolio theory, the book is useful to undergraduate students of mathematical finance, business and financial management.

“The book provides a holistic insight into mathematical portfolio theory and analysis at an undergraduate level. … This useful textbook provides students and teachers with new perspectives and novel approaches.” (Pavel Stoynov, zbMATH 1519.91001, 2023)

Siddhartha Pratim Chakrabarty is Professor at the Department of Mathematics, Indian Institute of Technology Guwahati, Assam, India. With a long and varied experience of teaching and undertaking research work in a wide spectrum of subareas of finance, including financial engineering, mathematical finance, computational finance, Monte–Carlo simulation, portfolio theory and financial risk management, he has offered two Massive Online Open Course (MOOC) courses through the National Program for Technology Enhanced Learning (NPTEL), on mathematical finance and mathematical portfolio theory. Professor Chakrabarty is very passionate about undergraduate research, which has led to several publications with his undergraduate students, many of whom have gone on to secure prestigious positions in academia, data science, entrepreneurship and investment banking. In 2020, he was a recipient of the Scholarship Scheme for Faculty Members from Academic Institutions 2020 by the Reserve Bankof India. A very active in professional services and outreach activities, Prof. Chakrabarty has supervised four Ph.D. students and published 46 research articles.

Ankur Kanaujiya is Assistant Professor at the Department of Mathematics, National Institute of Technology Rourkela, Odisha, India. After completing his Ph.D. in the area of computational finance, he joined Birla Institute of Technology Mesra, Ranchi, Jharkhand, India, under the Technical Education Quality Improvement Programme (TEQIP) III before he moved to his current position. Dr. Kanaujiya has worked extensively in the areas of computational and applied mathematics with an emphasis on finance.