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School and University


Edinburgh Academy 
Trinity College, Cambridge (Open Scholar, Senior Scholar, Kaesbey Scholar, First Class Honours in the Mathematical Tripos and Distinction in Part III of Mathematical Tripos).
Diploma in Statistics-University of Edinburgh (with distinction)


Professional Qualifications


Fellow of the Royal Society of Edinburgh (FRSE).

Fellow of Institute and Faculty of Actuaries (FFA)  and Certificate in Derivatives (of Faculty and Institute of Actuaries),

Fellow of Institute of Mathematics and its Applications (FIMA)

Chartered Mathematician (CMath),

Fellow of the Royal Statistical Society (FSS),

Member of the London Mathematical Society (LMS)



Equitable Life Payment Scheme :  compensation calculation for the With-Profts Annuitants (not for the non-WPAs)

WPA_Compensation_for_the_WPAs (not for the non-WPAs).htm



Equitable Life Presentation (regarding the pre-1992 with-profits annuitants) to MPs on Wednesday 14 September 2011






Summer of 2004, 2005, 2006, 2007, 2008, 2009, 2010 and 2012 supervisor of post-graduate MSc Projects in Actuarial Mathematics at Heriot-Watt University -see DISSERTATIONS including projects using C++ , VB and VBA. Projects have involved quantitative finance and stochastic methods (particularly guaranteed annuity options), mortality projection using Lee-Carter with the extension to allow for the cohort effect, the Heligman-Pollard  mortality model, ARIMA time-series methods, ‘realistic balance sheets’ of insurance companies, demutualisation of insurance companies, solvency of insurance companies (Solvency II), non-life insurance including run-off triangles, ruin theory.


In 2008, 2010, 2011, 2012 and 2013 supervisor in MSc Operational Research (Finance) at Edinburgh University - see  DISSERTATIONS  where the MSc Projects have involved Counterparty Credit Risk, Copulas, CDSs, CDOs, Interest Rate Swaps, modelling derivatives by Monte-Carlo simulation  in C++ and interfacing C++ code  and R code with EXCEL through using the xlw  'wrapper' and RExcel.


Consulting Actuary  - assignments have included those for Australian National Provident, Allianz-Dresdner, London legal firms and various Insurance Projects involving the use of Mathematical Finance and the valuation and ability to hedge (hedgeability) Guaranteed Annuity Rate (GAR) Options  - a type of so-called Exotic Option. Actuarial analysis of Equitable Life given without charge to Sir John Chadwick at his request.

In 2003 and 2005, Guest of Centre Nationale de la Recherche Scientifique (CNRS), Nice , France.

Two of the MSc Projects involved Financial Mathematics and stochastic methods see Quantitative Finance

The first of the above Projects involved the valuation and ability to hedge (hedgeability) of Guaranteed Annuity Rate (GAR) Options (a type of so-called Exotic Option) being programmed in C++.

The second of the above Projects involved the pricing and hedging of a monthly premium guaranteed maturity value on a unit-linked policy. This is a type of Asian Option but not the normal type of arithmetic or geometric Asian Option. This work seemed original as far as a monthly premium policy was concerned. The dynamic hedging required was shown interactively on an EXCEL spreadsheet with the programming being done in VB and VBA.




Senior lecturer in the Department of Actuarial Mathematics and Statistics, Heriot-Watt University.

Consulting actuary to a number of financial institutions.




Consulting actuary with PricewaterhouseCoopers (PwC), London, advising insurance companies and unit trust/ investment management companies.


From leaving university until 1996


Actuary with the Scottish Widows Fund and Life Assurance Society, Edinburgh including the post of Appointed Actuary.  


·        Head of Corporate Pensions and Pensions Strategy, 1995-96,

·        Appointed Actuary, 1992-95,

·        Head of Finance Division, 1991-93,


Involvement in the Actuarial Profession


·      Positions held within the Faculty of Actuaries at various times include:-


Member of Faculty Council,

Representative on the Groupe Consultatif  d’Actuaires des Pays des Communautés Européenes,

Representative on the International Actuarial Notation Committee,

Member of Faculty Examination Board,

Member of the Profession’s General Insurance Board,

Member of Profession’s Professional Affairs Board.

Chairman of Faculty Research Committee,  

Member of the Profession’s Continuous Mortality Investigation (CMI) Executive and  its Mortality Sub-Committee,

Chairman of Faculty’s Bonus Research Group,

Member of Profession’s Textbooks Committee,

Chairman of Profession’s Library Committee,

Faculty Tutor,

President of the Faculty of Actuaries Students Society.


·      External Examiner at Heriot-Watt University  (1983-88).


·      Vice-President of Institute of Mathematics and its Applications (2000-02),

Member of Council of the Institute of Mathematics and its Applications (1987-90) Chairman of the Scottish Branch of the Institute of Mathematics (1990-92).


·      Chairman of the James Clerk Maxwell Foundation and Trustee of the Foundation since 1992 The Foundation is the owner of Clerk Maxwell’s House at 14 India Street, Edinburgh.


·      Special Adviser, Council for National Academic Awards (1990-94).


Key Experience and Expertise


·        Expert knowledge of actuarial mathematics and business practice of life assurance and pensions,

·        Extensive experience of the management and running of life insurance companies,

·        Expert knowledge of actuarial and accounting matters as they relate to the insurance industry and to mergers and acquisitions e.g. product development and pricing, profitability analysis, valuation of companies through use of embedded/appraisal values, need for an estate in a with-profits fund with un-hedgeable guarantees and the smoothing of investment returns if the reasonable expectations of all policyholders is to be met, profit reporting, statutory and embedded value profits, UK and US GAAP, Australian Margin on Services, International Accounting Standards, Fair Value Accounting etc.

·        Extensive knowledge of stochastic methods including Professor Wilkie's Equations having employed stochastic methods since the late 1980s,

·        Extensive knowledge of the UK insurance industry in general and of individual companies in particular,

·        Good knowledge of the European insurance market and two European languages,

·        Expert knowledge of the demutualisations which have taken place in UK.

·        Extensive knowledge of UK pensions and knowledge of European pensions.

·        Knowledge of investment matters including quantitative methods in finance e.g. knowledge of the use of derivatives (futures, options, swaps, swaptions, caps, floors etc.) and the mathematics (stochastic calculus) underlying their pricing, and the use of derivatives in hedging out the risks of guarantees and options. The Certificate in Derivatives of the Faculty and Institute of Actuaries is held.

·        Good knowledge of mathematical statistics.





Fischer Black


Louis Bachelier


Thomas Bond Sprague





Author of some 52 articles/papers (see attached list below) on actuarial/insurance/financial/scientific matters and the contributions published on the websites below,  including 8 articles in “The Actuary” magazine, and 2 submissions to the H.M. Treasury regarding (1) the Morris Inquiry into the Actuarial Profession  and (2) the Myners Inquiry into Mutual Insurance Companies.


            Actuarial Analysis of the need for an Estate in a with-profits fund





also see article on 'Bivariate Normal' of 15 November 2004 on Mathfinance Newsletter             


Lectures/talks/other matters


·      On the Royal Society of Edinburgh's (RSE) Organising Committee for the conference 'Calculation in Finance and Insurance, post Napier' held in the RSE on 3rd April 2014 to mark the 400th anniversary of John Napier's invention of logarithms in 1614


·      Organised, jointly with the British Society for the History of Mathematics,  the meeting  'John Napier, the Historical  Legacy' held on 4th April 2014 in the premises of the James Clerk Maxwell Foundation, Edinburgh, to mark the 400th anniversary of John Napier's invention of logarithms in 1614.


·      Joint Organiser of a joint International Centre for Mathematical Sciences (ICMS)/Faculty of Actuaries seminar entitled ‘Realistic Valuation of Life Assurance Liabilities’ held at Royal Society of Edinburgh on 8 September 2004.


·      Honorary Treasurer of the company ICIAM99. ICIAM99 was a company whose Chairman was Sir Michael Atiyah, OM, PPRS, PPRSE.  ICIAM99 was set up to organise the International Congress of Industrial and Applied Mathematics in Edinburgh in July 1999.


·     Organiser of the Financial Mathematics Day at the above International Congress. This day of seminars was organised in conjunction with the Institute and Faculty of Actuaries.


·      Numerous lectures and talks given on actuarial/insurance matters both at home and abroad including talks in French and German.




·      Faculty of Actuaries Prize for paper ‘Studies of Reversionary Bonus using a Model Office’ (with P S Carr),


·      Faculty of Actuaries Prize for paper ‘On Graduation by Mathematical Formula’ (with J J McCutcheon and A D Wilkie),


·      Faculty of Actuaries Prize for paper  Developing an International Accounting Standard for Life Assurance Business’ (with N. Masters).



Published Professional Actuarial Papers



1980 - "Studies of Reversionary Bonus using a Model Office" (with P S Carr)- Transactions of the Faculty of Actuaries, 37


1987 -"The Changing Shape of English Life Tables" (with D M Smith)

- Transactions of the Faculty of Actuaries,  40


1987 - "Bonus Rates, Valuation and Solvency during the Transition between Higher and Lower Investment Returns" (with other authors)

- Transactions of the Faculty of Actuaries, 40


1988 -"On Graduation by Mathematical Formula" (with A D Wilkie and J J McCutcheon) -Journal of the Institute of Actuaries, 115  and Transactions of the Faculty of Actuaries, 41.


1988 - "A Stochastic Approach to Immunisation" (with D Paul)

- Proceedings of the 23rd International Congress of Actuaries, Helsinki.


1989 - "Using APL for Financial Calculations"- Journal of the Institute of Actuaries, 116


1995 - "(1) Some Aspects of the Actuarial Management of a Life Office.(2) Some Recent Trends in the UK Life Market which have Actuarial Implications"- Proceedings of the Professor Alexander Craig Aitken Centenary Conference, Otago University, New Zealand.


1998 - "History of the development of the actuarial profession and of actuarial thought in Scotland" - Transactions of the 26th International Congress of Actuaries .


1998 - "Report on the oncoming revision of the EU solvency regime" (with other authors) - Transactions of the 26th International Congress of Actuaries.


1999 - “Developing an International Accounting Standard for Life Assurance Business” (with N. Masters) – British Actuarial Journal, 5.


1999 - Projection Factors for Mortality Improvements” (with J J McCutcheon) -Continuous Mortality Investigation Report, 17.


2004 –Six articles entitled :- "Asset Shares, Capital in Life Assurance, Early Mortality Tables, History of Actuarial Education, Life Table and Mortality Laws" in Encylopedia of Actuarial Science, John Wiley and Sons, Chicester, England.,


2006 - "Five Parameter Approach to Mortality in Ancient Times" - Actes des 8e Journees Anthropologiques de Valbonne, eds. Buchet L., Dauphin C., Seguy I.


2009 -"Forecasting U.K. Population Mortality allowing for Age, Period and Cohort Effects", British Actuarial Journal, 15, 73-89.


2012 - "Actuarial Functions on many correlated lives" (submitted to Annals of Actuarial Science)



Authorship of actuarial booklets produced by the Faculty and the Institute of Actuaries



1986 - "The Mathematics of Profit Testing for Conventional and Unit-Linked Business" (with A Gupta)


1986 - "A Stochastic Approach to Life Contingencies" (with H Waters)



Other Publications



1986 -  "Independence and the Length of a Run of Wins" (with T W Keogh) - Mathematical Spectrum, Volume 18


1986 - "On a Certain Diophantine Equation" (with J J McCutcheon)

- Mathematical Gazette, Vol 70


1987 - "Are Traditional Valuation Methods still appropriate?" - Proceedings of Life Office Valuation Seminar - published by Institute of Actuaries.


1989 - "APL for Financial Calculations in Insurance" - Vector Vol 6 No 3


1992 - "The Origins of the Clerk Maxwell Genius" - Bulletin of the Institute of Mathematics and its Applications - January/February 1992, 28, Nos 1/2


1992 - "The Impact on Solvency and Policy Results of the Valuation Regulations" - Proceedings of Seminar on Financial Reporting for Life Assurance - London


1996-,"What became of the Senior Wranglers?" - Mathematical Spectrum, Volume 29, No 1


1996 -  "How others see us ...... en français" - The Actuary Magazine – April.


1998 - "Financial Condition Reports" - The Actuary Magazine - April


1998 - "Accounting for deferred acquisition costs" - The Actuary Magazine – April.


1998 "Mortality" - Ivanhoe Career Guide for Actuaries published by Cambridge Market Intelligence


1999 - “Generations of Genius” – article published in James Clerk Maxwell Commemorative booklet produced by the James Clerk Maxwell Foundation.


1999 - “The remarkable story of Maxwell and Tait” article published in James Clerk Maxwell Commemorative booklet produced by the James Clerk Maxwell Foundation.


1999 “Fair Value of Liabilities” -The Actuary Magazine, October  


2001 – “The Remarkable Story of Maxwell and Tait,  Scottish Mathematical Council Journal , 30, 60-65.


2002- “James Clerk Maxwell: his qualities of mind and personality” –Mathematics To-day, 38, 3.


2003 -Contribution to the paper "Reserving, Pricing and Hedging for Policies with Guaranteed Annuity Options", British Actuarial Journal, 9, 412-418


2005 - ”What assurance did the guarantees provide”-Actuary Magazine, April 2005


2005  - Contribution on the actuarial meeting on "The Penrose Report”,  British Actuarial Journal, 10,1066-1070.


2006 - “Back to the Future” –Actuary Magazine, January/February 2006


2006 “Serving the Public Interest” –Actuary Magazine, July 2006 (Part I of article) and August 2006 (Part II)


2006 - Contribution to paper "Living with Mortality: Longevity Bonds and other Mortality-Linked Securities", British Actuarial Journal, 12, 203-205


2008 “The Estate and the FSA Principles”, - Actuary magazine, June 2 2008


2009 "Celebrating the Achievements and Legacy of James Clerk Maxwell", author of chapter  "Clerk Maxwell and the Royal Society of Edinburgh", and editor of the book published by the Royal Society of Edinburgh.


2010 “The story of ‘le pli cacheté’, number 11.668 or did Wolfgang Döblin’s discoveries include a version of Itô’s Formula?, Mathematical Spectrum, Volume 42,129-133.


Other articles and papers



1987 - "The Changing Shape of Mortality 1689-2001" - paper presented at seminar Heriot-Watt University


1988 - "Regional and Occupational Variations in Group Life Mortality" - paper presented to meeting 'Developments in Life Insurance' - Heriot-Watt University


1991 - "Some Applications of APL to the Valuation of Cash Flows"

- APL Conference in California


1991 - "Aufsichtstrukturen and Marktumfeld in Grossbritannien"

- presented at Life Insurance Seminar in Cologne, Germany .


1991 - "Investments - United Kingdom" - presented at International Summer School organised by Groupe Consultatif - Edinburgh


1991 - "Reserving and Valuation - United Kingdom" - presented at International Summer School organised by Groupe Consultatif - Edinburgh


1993 – “Risk Based Capital Report” by Joint Actuarial Working Party of Faculty and Institute of Actuaries- chaired by Hylands J.F.


1993 - "Abolition of State Premium Control?  How to protect the consumer now?  What can the UK experience tell us?

- paper presented at seminar on 'A Free European Market and Consumer Protection - a Contradiction in itself' - Berlin


1994 - "Using APL for Financial and Actuarial Calculations" - Proceedings of APL in Business Conference - Swansea


1995 - "James Clerk Maxwell - Maker of Waves" - presented at conference 'Scotland's Mathematical Heritage' - Royal Society of Edinburgh


2000 –Comments on FASB document  Statement of financial accounting concepts No. 7 – using cash flow information and present value in life accounting measurement” for Life Board of Faculty and Institute of Actuaries


2006 –“Annuity rate guarantees under U.K. with-profits policies”, examines guaranteed annuity rates (GARs), from the mathematical finance point of view, and the different effect of (a) applying the GAR option to the contractual benefits only or (b)  applying the GAR to the whole maturity proceeds of the policy i.e. including contractual and non-contractual (terminal bonus) benefits.  



Glossaries -Actuarial

Glossaries- Options and Futures


Other Web-sites of interest


Actuarial Profession - Faculty of Actuaries and Institute of Actuaries


Actuarial Mathematics & Statistics


The Actuary - The magazine of the actuarial profession


Actuarial Profession - Continuous Mortality Investigation (CMI)


Groupe Consultatif Actuariel Europeen