Photo of Mike OsborneMike Osborne
Honorary Senior Lecturer (Accounting and Finance)


My research is based on a particular manifestation of a general principle: the principle is duality and the manifestation involves the polynomial. Given the fundamental theorem of algebra, a set of n numbers in the real domain may be entered as coefficients into a polynomial and the polynomial factorized to produce a unique set of n different numbers (roots) in the complex domain. This transformation allows problems couched in terms of real numbers to be recast in terms of their complex counterparts; thus, a real problem transforms into its complex dual. While solutions to real problems may be elusive, solutions to their duals may sometimes be found. Polynomials are ubiquitous in financial economics, and therefore duality may offer solutions to some financial problems; this possibility has driven my research for over thirty years.

More specifically, my research investigates the use and meaning of all solutions (interest rates) to the time value of money equation. The research attempts to understand interest rates that have been ignored by economists for centuries. The time value of money features in many areas of financial economics, and therefore the research has a variety of applications in economic theory, capital budgeting, retail & corporate finance, fixed income mathematics, and behavioural economics. More recently, duality applied to statistical theory has become an interest.

Some of the research is summarised in the book 'Multiple Interest Rate Analysis' published in January 2014 by Palgrave Macmillan:

'I liked everything about it (except for the title, which gave me no clue about what was inside). If anyone had asked me, I would have guessed that there was nothing very new to be said about present-value equations, but you have certainly showed that conjecture to be wrong. The product of the roots of the present-value polynomial contains interesting and useful information, as the book demonstrates'. Robert M. Solow, Nobel Laureate in Economics (1987), Institute Professor, Emeritus, and Professor of Economics, Emeritus, Massachusetts Institute of Technology.

'When facing complex problems that arise in the real world, one should always remember that real answers to real questions may require imagination. This book gets to the real root of such problems and more.' Peter Carr, PhD, Department Chair, Finance and Risk Engineering, Tandon School of Engineering, New York University.

'This is seminal stuff. The material in this book should have been discovered in the 1930s, 1940s, or 1950s. Instead, it managed to evade capture until very recently. I regret not having had access to this book in the 1980s, when I first worried about these and related issues as a graduate student. I thought at that time that no further resolution existed. So, this book was an eye opener for me. It is difficult to overemphasize the importance of Osborne’s work in finally putting into place that last missing piece of a jigsaw puzzle handed down from generations of previous financial economics researchers. Osborne carefully explains why multiple-interest-rate solutions to TVM equations are important, even those pesky large negative or complex-valued outcomes that other researchers are all too eager to discard.' Timothy Falcon Crack, PhD, Professor of Finance, University of Otago, New Zealand.

A computable document written in Mathematica is available in the Wolfram Demonstrations Project at The document enables dynamic illustrations of many examples in the book.

A recent Tedx talk gives the flavour of the research via one of its many applications (retail finance):

Various research papers are in SSRN at and in REPEC at PhD thesis is in the Middlesex University research repository at



2014     Multiple Interest Rate Analysis: Theory and Applications, Palgrave Macmillan, ISBN 978-1-137-37276-5,

Journal articles

2016     (with Ian Davidson) The Cambridge controversies in the theory of capital: contributions from the complex plane, The Review of Political Economy, 28(2), 

2015     (with Edward O’Reilly) A Model Illustrating Multiple Interest Rate Analysis (MIRA), Wolfram Demonstrations Project.

2010     A resolution to the NPV-IRR debate? Quarterly Review of Economics and Finance, 50(2).

2005     On the computation of a formula for the duration of a bond that yields precise results, Quarterly Review of Economics and Finance, 45(1), 

2003     (With Mark Osborne) A polynomial that is a statistical prism, Mathematical Gazette, 87(508) 

2001     Three extensions to the visualisation of financial concepts in the complex plane, Computers in Higher Education Economics Review, 14(2), 

2000     Visualizing financial concepts in the complex plane, Computers in Higher Education Economics Review, 14(1), 

1993     Chaos and the internal rate of return, Computers in Higher Education Economics Review, 7(19), 

1990     Financial chaos, Management Accounting, 68(10)

1989     On Popper, education and training, Banking and Financial Training, 5(1)

1989     On the marginal cost of a student in the public sector of higher education in the UK, Journal of Further and Higher Education, 13(1) 

1984     On the presentation of IS-LM analysis, The Indian Economic Journal, 32(1) 

1982     (With Brian Snowdon) Inflation and unemployment, Chap. 3, What sort of society? Elcock, G. (ed.), Martin Robertson, ISBN 0-85520-524-5

Working papers

2024 Reswitching Redux. SSRN.
2024 A Financial Fable. SSRN.
2022 Exponential growth bias and Consumer Credit Legislation. SSRN.
2022 On exponential and hyperbolic discounting. SSRN.
2022 (with Timothy Crack, Malcolm Crack, and Mark Osborne) A new approach to Student and Fisher using polynomial roots. SSRN.
2014 Exponential versus Hyperbolic Discounting: A Theoretical Analysis. SSRN.
2011 A note on Macaulay’s formula for duration. SSRN.
2011 An essay on the inadequacy of APR as a measure of the cost of consumer credit, and why consumer credit legislation should be revised. SSRN.
2010 On the meaning of internal rates of return and why an internal rate of return is not an investment criterion. SSRN.
2010 The Cambridge controversies in the theory of capital: a solution to the reswitching puzzle. SSRN.
Conference presentations
2024 Exponential Growth Bias and Consumer Credit Legislation. 17th Conference of the Behavioural Finance Working Group, London. 6-7 June.
2015 Exponential versus hyperbolic discounting: a theoretical analysis. 3rd Conference of the Behavioural Finance Working Group on Financial Regulation, Queen Mary University London, 11-12 June.
2013 (with Ian Davidson) The Cambridge controversies in the theory of capital: contributions from the complex plane. 15th Conference of the Association for Heterodox Economics, London Metropolitan University, 4-6 July.
2011 On the significance of Sraffa's reswitching: some long-standing financial puzzles and their joint resolution. Cambridge Keynes Seminar, Robinson College, University of Cambridge, 15 February.
2005 A simple, accurate formula for the duration of a portfolio of bonds under a non-parallel shift of a non-flat yield curve. International Conference on Finance, Finance Research Unit, University of Copenhagen, Copenhagen, Denmark, 2-5 September.
2004 On the computation of a new formula for the duration of a bond that yields precise results without the need for convexity and other devices. 53rd Annual Conference of the Midwest Finance Association, Chicago, Illinois, USA, 18-20 March.
2002 A fresh look at the time value of money equation.15th Australasian Finance & Banking Conference, University of New South Wales, Sydney, Australia, December.
2001 On the time value of money equation and its application to risk. In: 3rd International Conference on Money, Investment & Risk, Nottingham Trent University, 1-2 November.
2001 A new approach to interest rate sensitivity using the complex plane. In: Proceedings of the International ICSC Congress on Computational Intelligence: Methods and Applications (CIMA'2001), Advanced Computing in the Financial Markets, University of Wales at Bangor, 19-22 June.
1996 The impact of some market research on the design of a training program for the wholesale financial markets. Proceedings: International Conference on `Finance & Banking Training in the Modern World', Moscow, Russia, September.