Research Publications
Books
Journal Articles
Books

Social Aggregations and Distributional Ethics.
(with M. Mitra and S. Mutuswami)
Cambridge University Press, Forthcoming.

An Introduction to Algorithmic Finance, Algorithmic Trading and Blockchain.
(with P. Sarkar)
Bingley, United Kingdom: Emerald Publishing Limited, 2020, pp.191
    *This book provides a broad-based, accessible introduction to three of the most important areas of computational finance, namely, option pricing, algorithmic trading and blockchain. Highlighting and explaining the current phenomena in algorithmic finance in an articulate manner, this book provides the basic understanding required for a career in the finance industry and for more specialized courses in finance. Divided into three clearly structured parts, it provides the necessary theoretical background on derivatives, options and stochastic dominance, it covers various algorithmic issues of finance, discussing specific algorithms, their applications and consequences, and complementing these two sections, it discusses recent developments in blockchain and cryptocurrency. For its clear structure and exhaustive coverage of the essentials, this book is a must-read for students of finance and for finance professionals, and it is of interest to anyone interested in or invested in the finance industry.

Poverty, Social Exclusion and Stochastic Dominance.
Singapore: Springer Nature, 2019, pp.259
    *This collection of essays honors the memory of Tony Atkinson, who made significant contributions to the rigorous study of income inequality, poverty and redistribution. These essays, covering a span of over thirty years of research and scholarship, have been at the forefront of distributional analysis, and many of them are of prime importance for contemporary developments in the real-valued measurement of poverty and inequality, with particular reference to the notions of fuzzy poverty assessment, endogenous poverty threshold, heterogeneity/multidimensionality, unit-consistency, sub-group decomposability, and dominance criteria. While all of these articles have been previously published – singly or with co-authorship – in a number of scholarly professional journals or distinguished edited volumes, this collection is greatly enriched by a substantial authorial introduction, which places the contributions in context, highlights their inter-connectedness, and relates them to the work of Tony Atkinson and other scholars. This book is of intrinsic value to welfare analysts, as well as being a tribute to a very great scholar by a fellow-economist.

Analyzing Multidimensional Well-Being: A Quantitative Approach.
New Jersey: John Wiley & Co., 2018, pp.319.
    A very important development in human well-being research in recent years is the shift of emphasis from a single dimension to multidimensional frameworks. This book considers multidimensional proposals to the assessment of welfare, inequality, poverty and vulnerability. The main approach adopted in the monograph is axiomatic. A systematic comparison of alternative recommendations to the evaluation of multidimensional welfare is presented in Chapter 1. It is clearly argued that multidimensional analysis is intrinsically different from the marginal distributions-based analysis, since the latter does not capture the essence of multidimensionality entirely. In Chapter 2 there will be an extensive inquiry into both descriptive and welfare theoretic suggestions to the judgment of multiattribute inquality. Chapter 3 provides a synthesis of multidimensional poverty analysis. It is clearly indicated that for qualitative data a different axiomatic structure is needed. Another highly important concern of the chapter is multidimensional poverty dominance. Chapter 4 deals with applications of fuzzy sets to the determination of multididimensional poverty whenever the possibility of lack of relevant information on achievement quantities arises. Often it becomes necessary to gauge poverty chronically using panel data instead of restricting attention to a single period. This issue is investigated in details in Chapter 5. The concern of Chapter 6 is an appraisal of multidimensional vulnerability to poverty. To show real life applications of some multidimensional aggregations, Chapter 7 analyzes some composite indices; most of which have been designed by international organizations such as The United Nations Development Program, The Organization for Economic Co-operation and Development and The World Bank; to judge performance of a country in different dimensions of well-being from different perspectives. Important policy recommendations may be driven from the studies carried out in the chapters.

Inequality, Polarization and Conflict: An Analytical Study.
New York: Springer, 2015, pp.137.
    The study of polarization is crucial for understanding the economic wellbeing,economic growth and social cohesion of the population of a country.This book begins by presenting an an up-to-date systematic treatment of bipolarization and multigroup polarization using income as the attribute of human well-being. Within the framework of bipolarization, both welfare theoretic approaches and descriptive approaches that do not make use of a concept of social welfare, are discussed.Apart from discussing indices under alternative notions of polarization invariance(e.g., ratio scale, absolute scale, intermediate scale, unit consistency) in this framework, there will be analysis as well on polarization orderings.Seemingly unrelated and intuitvely reasonable conditions consistent with polarization orderings are also presented. Using the notions of identification and alienation, a detailed discussion on multigroup polarization is presented. Reduced-form indices that are based on two summary statistics of income distributions, the within and between-group components of inequalty, and an associated ordering are examined analytically. Social polarization that results in differentiation across social groups is of long-standing interest to many because widening gaps may lead to high economic and humanitarian costs. Therfore, an important concern of the book is the measurement of social polarization. Since the wellbeing of a population depends on many nonincome indicators of human life, which are represented by ordinal varibles like health and litercay statuses, a formal treatment of polarization for an ordinal variable will also be provided. Finally, there will be a summary of relevant research on fractionalization, polarization and likelihood of conflict in one chapter.

A Course on Cooperative Game Theory.
(with M. Mitra and P. Sarkar)
Cambridge: Cambridge University Press, 2015, pp.268.
    Cooperative game theory deals with real life situations where objectives of the participants are partially cooperative and partially conflicting. To motivate the chapters, the book begins with a non-technical discussion and several illustrations. The solution concepts discussed at the outset are the core, which requires that no set of players can leave and take a collective action that will make them better off, the stable sets that rely on stability of the payoff vectors, the bargaining sets that are based on threats and counter-threats, the kernel which is dependent on comparative importance of players in coalitions and nucleolus that rests on comparisons among the excesses of different payoff vectors. The Shapley value which represents an expected payoff from participation in a game and the Weber set being a set valued extension of the Shapley value are discussed then. Voting games which are necessary to understand the voting situations that arise in decision making bodies like the UN Security Council and the European Union are discussed rigorously. Finally, mathematical matching problem whose objective is to propose a good matching system for the participants, computational aspects of cooperative game theory and bargaining models are presented. Each chapter will contain several applications and numerical examples.

An Outline of Financial Economics.
New York, London, New Delhi: Anthem Press,
2013, pp. 315. Reprinted in 2014.
    This book presents a systematic treatment of the theory and methodology of finance and economics. The book follows an analytical and geometric methodology, explaining technical terms and mathematical operations in clear, nontechnical language, and providing intuitive explanations of the mathematical results. It begins with a discussion of financial instruments, which form the basis of finance theory, and goes on to analyze bonds - which are regarded as fixed income securities - in a simple framework and to discuss the valuation of stocks and cash flows in details. Highly relevant topics like attitudes towards risks, uncertainty, financial structure of a firm, stochastic dominance, portfolio management, capital asset pricing model, conditions for non-arbitrage, risk-neutral valuation and the methods for determining prices of different types of options, which give the right to buy or sell an asset, are analyzed explicitly.

Econophysics of Income and Wealth Distributions.
(with B. K. Chakrabarti, A. Chakraborti and A. Chatterjee)
Cambridge: Cambridge University Press, 2013, pp.224.
    The distribution of wealth and income is never uniform, and philosophers and economists have tried for years to understand the reasons and formulate remedies for such inequalities. This book introduces the elegant and intriguing kinetic exchange models that physicists have developed to tackle these issues. This is the first monograph in econophysics focussed on the analyses and modelling of these distributions, and is ideal for physicists and economists. It is written in simple, lucid language, with plenty of illustrations and in-depth analyses, making it suitable for researchers new to this field as well as specialized readers. It explores the origin of economic inequality and examines the scientific steps that can be taken to reduce this inequality in the future.

Inequality, Polarization and Poverty: Advances in Distributional Analysis.
New York: Springer, 2009, pp.187
    The study of inequality, polarization and poverty is crucial for understanding the economic well-being of the population of a country. Conceptual and methodological advances and better data have provided greater insights into these issues in recent years, and it is the objective of the book to present a systematic and up-to-date treatment of the developments in the subject. Both welfare theoretic and descriptive approaches are discussed and, since the well-being of a population depends on income and non-income indicators, both uni-dimensional and multi-dimensional frameworks are taken into consideration. The technical and mathematical operations employed to analyze the results are explained intuitively in non-technical terms, and numerical analyses and graphical representations help to illustrate important concepts.

Ethical Social Index Numbers.
Berlin, Heidelberg,Hong Kong, London, New York, Paris, Tokyo:
Springer-Verlag, 1990, pp 322.
( Electronic Edition, 2012 )
    The subject of this book is income distribution-based social index numbers.These index numbers quantify different aspects of income distribution data. The topics covered are: inequality, economic distance, relative deprivation, poverty, tax progressivity, horizontal inequity and mobility. The main purpose of the book is to present the significant results on welfare theoretic approaches to income distribution based measurement problems. Discussions of descriptive approaches, which do not make use of a concept of social welfare, are also included. Thus, the book gives an overall view of the recent developments in this subject. The technical terms and mathematical operations employed to discuss the results are explained in non-technical terms, and intuitive explanation of the mathematical results are given. Numerical illustrations of some of the results are provided using income distribution data.

    Issues in Industrial Economics.
    Aldershot, Brookfield, Hong Kong, Singapore, Sydney:
    Avebury Publishing, 1995, pp 183.
    Reprinted in 1996.

A major concern of industrial economics is market power, the ability of firms to set prices above the competitive level. One of the main purpose of this book is to analyze market power from different perspectives. In particular, its implications (in terms of welfare, firm diversification etc.), relationship with concentration, game theoretic explanation and efficiency hypothesis (Chicago School's view) are considered explicitly. Procedures for analyzing the efficiency of a merger and welfare are investigated. Various issues on concentration and efficiency are discussed elaborately. In the context of a structure-conduct-performance paradigm, the theoretical as well as empirical aspects of issues like profitability - concentration relationship, contestability, entry of firms and entry barriers are explored. Alternative attempts to generate size distribution of firms are examined in detail. Several topics on policy matters are also considered. All technical terms and mathematical results are supplemented by intuitive explanations.

    Microeconomics.
    Bangalore, Chennai, Hyderabad, Kolkata, New Delhi:
    Allied Publishers Pvt Ltd.  2002,  pp.782.
    Reprinted in 2004, 2005, 2008, 2010, 2012, 2016, 2019.
This book adopts an analytical and geometric methodology in the presentation of the text. Since the main text is comparatively free of mathematics, many chapters have been supplemented by mathematical appendices. Each chapter also contains applied examples directly related to the theoretical issues discussed in the text. Different types of exercises like multiple choice, prove-disprove questions, and quantitative problems and questions are also included. In addition to covering traditional aspects of microeconomics, the book also discusses some recent developments like game theory, externalities, public good, information and law. Also, topics such as linear models, theory of distribution, and international trade, which are not usually found in texts on microeconomics, have been discussed.

This book should be useful as class material for undergraduate and graduate students of economics and business.

    Edited Books:

    (1) Econophysics & Economics of Games, Social Choices and Quantitative Techniques(with Banasri Basu, Bikas K. Chakrabarti, and Kausik Gangopadhyay), Springer-Verlag, Italia, 2009.


    (2) Quantitative Economics: Theory and Practice, Essays in Honor of Professor N. Bhattacharya, Allied Publishers, New Delhi, 1998, pp.370.


Journal Articles

Research papers have come out in some of the most prestigious and high-impact journals in Economics, including Econometrica, Journal of Economic Theory, International Economic Review, Journal of Development Economics, Social Choice and Welfare, Canadian Journal of Economics , Games and Economic Behavior, Economic Theory, Journal of Economic Inequality, Mathematical Social Sciences, Theory and Decision, Health Economics and Review of Income and Wealth.

A list of selected publications is given below.

  1. ‘New Perspectives on the Gini and Bonferroni Indices of Inequality’ (with P. Sarkar), Social Choice and Welfare, Forthcoming.

  2. ‘An Inequality Paradox: Relative versus Absolute Indices?’ (with P. Sarkar), Merton 79, 2021.

  3. ‘On the probability Ratio Index as a Measure of Electoral Competition’(with M.Mitra, S. Mtuswami, and R. Pal ), Palgrave Communications-Nature 6, Article No. 96, 2020.

  4. ‘Pro-poorness Orderings’ (with N. Chattopadhyay and C. D’Ambrosio), Review of Income and Wealth 65, 2019.

  5. ‘Measuring Chronic Multidimensional Poverty’ (with S. Alkire, M. Apablaza and G. Yalonetzky), Journal of Policy Modeling 39, 2017.

  6. ‘On a Family of Achievement and Shortfall Inequality Indices’ (with N. Chattopadhyay and C. DÁmbrosio), Health Economics 25, 2016.

  7. ‘Reference Groups and the Poverty Line: An Axiomatic Approach with an Empirical Illustration’ (with N. Chattopadhyay, J. Deutsch, Z. Nissanov and J. Silber), Research in Economic Inequality 24, 2016.

  8. ‘Generalized Gini Polarization Indices for an Ordinal Dimension of Human Well-Being’ (with B. Maharaj), International Journal of Economic Theory 11, 2015.

  9. ‘Richness Orderings’ (with A. Bose and with C. D’Ambrodio), Journal of Economic Inequality 12, 2014.

  10. ‘An Axiomatic Approach to the Measurement of Poverty Reduction Failure’ (with C. D’Ambrodio), Economic Modeling 35, 2013.

  11. ‘Financial Inclusion in India: An Axiomatic Approach’ (with R. Pal), Journal of Policy Modeling 35, 2013.

  12. ‘Multidimensional Poverty and Material Deprivation with Discrete Data’ (with W. Bossert and C. D ’Ambrosio), Review of Income and Wealth 59, 2013.

  13. ‘Stochastic Dominance Relations for Integer Variables’ (with C. Zoli), Journal of Economic Theory 147, 2012.

  14. ‘Poverty and Time’ (with W. Bossert and C. D’Ambrosio), Journal of Economic Inequality 10, 2012.

  15. ‘Ethnic Polarization Orderings and Indices’ (with B. Maharaj), Journal of Economic Interaction and Coordination 7, 2012.

  16. ‘Measuring Ethnic Polarization’ (with B. Maharaj), Social Choice and Welfare, 37, 2011.

  17. ‘A Reconsideration of the Tradeoffs in the New Human Development Index’, Journal of Economic Inequality 9, 2011.

  18. ‘Polarization Ordering of Income Distributions’ (with C. D’Ambrosio), Review of Income and Wealth 56, 2010.

  19. ‘Minimal-Axiom Characterization of the Coleman and Banzhaf Indices of Voting Power’ (with R. Barua and S. Sarkar), Mathematical Social Sciences 58, 2009.

  20. ‘Equity and Efficiency as Components of a Social Welfare Function’, International Journal of Economic Theory 5, 2009.

  21. ‘On the Watts Multidimensional Poverty Index and its Decomposition’ (with J. Deutsch and J. Silber), World Development 36, 2008.

  22. ‘Millennium Development Goals: Measuring Progress towards Their Achievements’ (with A. Majumder), Journal of Human Development 9, 2008.

  23. ‘A Deprivation-based Axiomatic Characterization of the Bonferroni Index of Absolute Inequality’, Journal of Economic Inequality 5, 2007.

  24. ‘A Generalized Index of Employment Segregation’ (with J. Silber), Mathematical Social Sciences 53, 2007.

  25. ‘Population Growth and Poverty Measurement’ (with R. Kanbur and D. Mukherjee), Social Choice and Welfare 26, 2006.

  26. ‘The Measurement of Social Exclusion’ (with C. D’Ambrosio), Review of Income and Wealth 52, 2006.

  27. ‘On the Coleman Indices of Voting Power’ (with R. Barua and S. Roy), European Journal of Operational Research 171, 2006.

  28. ‘Measuring Human Poverty: A Generalized Index and an Application Using Basic Dimensions of Life and Some Anthropometric Indicators’ (with A. Majumder), Journal of Human Development 6,2005.

  29. ‘A Characterization and Some Properties of the Banzhaf-Coleman-Dubey-Shapley Sensitivity Index’ (with R. Barua, S. Roy and P. Sarkar), Games and Economic Behavior 49, 2004.

  30. ‘Individual Welfare, Social Deprivation and Income Taxation’ (with P. Moyes), Economic Theory 21, 2003.

  31. ‘Measurement of Multidimensional Poverty’ (with F. Bourguignon), Journal of Economic Inequality 1, 2003.

  32. ‘A Generalized Human Development Index’ Review of Development Economics 7, 2003.

  33. ‘Measures of Relative Deprivation and their Meaning in terms of Social Satisfaction' (with D. Mukherjee), Theory and Decision 47, 1999.

  34. ‘Efficient Horizontal Mergers’, Journal of Economic Theory 82, 1998.

  35. ‘On The Family of Subgroup and Factor Decomposable Measures of Multidimensional Poverty' (with D. Mukherjee and R. Ranade), Research on Economic Inequality 8, 1998.

  36. ‘On Shorrocks' Reinvestigation of the Sen Poverty Index', Econometrica 65, 1997.

  37. ‘Achievement and Improvement in Living Standards' (with A. Majumder), Journal of Development Economics 50, 1996.

  38. ‘The Optimum Size Distribution of Firms’, Mathematical Social Sciences 18, 1989.

  39. ‘Extended Gini Indices of Inequality', International Economic Review 29, 1988.

  40. ‘A Note on Measures of Distance between Income Distributions' (with B. Dutta), Journal of Economic Theory 41, 1987.

  41. ‘Ethical Indices of Income Mobility' (with B. Dutta and J. A. Weymark), Social Choice and Welfare 2, 1985.

  42. ‘Measurement of Fuzziness: A General Approach’ (with T. Roy), Theory and Decision 19, 1985.

  43. ‘Ethically Flexible Measures of Poverty', Canadian Journal of Economics 16, 1983.

  44. ‘A New Index of Poverty', Mathematical Social Sciences 6, 1983.


    45. Selected Articles in Edited Volumes

  45. ‘’An Axiomatic Analysis of Generalized Gini Air Quality Indices”, in N. Mukhopadhyay and P .P. Sengupta (eds.) Contemporary Research on Gini’s Inequality Index and Beyond, CRC Press (Taylor and Francis Group), Florida, 2021.

  46. ‘Multidimensional Poverty and Material Deprivation: A Theoretical Analysis’ (with N. Chattopadhyay), in C. D’ Ambrosio (ed.) Handbook of Research on Economic and Social Well-Being, Edward Elgar Publishing, Northampton, MA, USA, 2018.

  47. ‘Multidimensional Indicators of Inequality and Poverty’ (with M.A .Lugo), in Marc Fleurbaey and Matthew Adler (eds.) Oxford Handbook of Well-Being and Public Policy, Oxford University Press, New York, 2016.

  48. ‘Measuring the Impact of Vulnerability on the Number of Poor: A New Methodology with Empirical Illustrations’ (with N. Chattopadhyay, J. Silber and G. Wan), in J. Silber and G Wan (eds.) The Asian “Poverty Miracle”: Impressive Accomplishments or Incomplete Achievements?, Edward Elgar Publishing, Northampton, MA, USA, 2016.

  49. ‘A Poverty Line Contingent on Reference Groups: Iimplications for the Extent of Poverty in Some Asian Countries’ (with N. Chattopadhyay and J. Silber), in J. Silber and G Wan (eds.) The Asian “Poverty Miracle”: Impressive Accomplishments or Incomplete Achievements? ,Edward Elgar Publishing, Northampton, MA, USA, 2016.

  50. ‘Measuring Vulnerability to Poverty: An Expected Poverty Index’ (with N. Chattopadhyay), in R. P. Kundu, S. Subramanian and S. Ghatak (eds.) Contributions to Economic Analysis: Essays in Honor of Satish Jain, Routledge, London, 2015.

  51. ‘Intertmporal Material Deprivation’ (with W. Bossert, L. Ceriani and C. D’Ambrosio), in G. Betti and A. Lemmi (eds.) Poverty and Social Exclusion: New Methods of Analysis, Routledge, London, 2013.


  52. ‘A Family of Unit Consistent Multidimensional Poverty Indices’ (with C. D’Ambrosio), in V. Berenger and F. Bresson (eds.) Monetary Poverty and Social Exclusion around the Mediterranean Sea, Springer, New York, 2012.


  53. ‘Inequality and Polarization: An Axiomatic Approach’ (with N. Chattopadhyay and B. Maharaj), in J. Silber and J. Deutsch (eds.) Measurement of Individual Well-Being and Group Inequalities, Rutledge, London, 2010.


  54. ‘Metodologia de la medicion multidimensional de la pobreza para Mexico’, in Minor Mora (ed.) Medicion Multidimensional de la pobreza en Mexico, El Colegio de Mexico, Mexico City, 2010.


  55. ‘Generalized Gini Occupational Segregation Indices’ (with C. D’Ambrosio and J. Silber), in Y. Fluckiger, Sean F. Reardon J. and Silber (eds.) Occupational and Residential Segregation, Emerald, London, 2009.


  56. ‘Multidimensional Poverty Orderings: Theory and Application’ (with F. Bourguignon), in K. Basu and R. Kanbur (eds.) Arguments for a Better World: Essays in Honor of Amartya Sen (Volume I: Ethics, Welfare and Measurement), Oxford University Press, London, 2008.


  57. ‘Measuring Multidimensional Poverty: The Axiomatic Approach’ (with J. Silber), in N. Kakwani and J. Silber (eds.) Quantitative Approaches to Multidimensional Poverty Measurement, Palgrave MacMillan, London, 2008.


  58. ‘An Axiomatic Approach to Multidimensional Poverty Measurement via Fuzzy Sets’, in G. Betti and A. Lemmi(eds.) Fuzzy Set Approach to Multidimensional Poverty Measurement, Springer, New York, 2006.


  59. ‘Intersociety Literacy Comparisons’(with A. Majumder),in Mark McGillivray (ed.) Inequality, Poverty and Well-being ,Palgrave Macmillan, London, 2006.


  60. ‘Measuring Inequality: The Axiomatic Approach' in J. Silber (ed.) Handbook of Income Inequality Measurement, Kluwer Academic, Boston, 1999.


  61. ‘A Family of Multidimensional Poverty Measures' (with F. Bourguignon), in D. J. Slottje (ed.) Advances in Econometrics, Income Distribution and Methodology of Science : Essays in Honor of Professor Camilo Dagum, Springer-Verlag, New York, 1999.


  62. ‘Measurement of Income Inequality: Observed Versus True Data' (with W. Eichhorn), in W. Eichhorn (ed.) Models and Measurement of Welfare and Inequality, Springer, New York, 1994.


  63. ‘Oligopolies and Aggregate Market Power’, in W.E. Diewert et al.(eds.) Mathematical Modeling in Economics, Essays in Honor of Professor W . Eichhorn, Springer, New York, 1993.


  64. ‘Axiomatizations of the Entropy Numbers Equivalent Index of industrial Concentration’ (with J.A. Weymark), in W. Eichhorn(ed.) Measurement In Economics, Physica- Verlag, Heidelberg, 1988.