Abstract
Coming at the end of the Renaissance period and some 100 years after the Reformation, the mid-seventeenth century is generally regarded by historians as part of the early modern epoch. We should not, however, infer from this label that for Britain it was a time of stability in its political institutions or sophistication in its financial institutions. England spent the middle of the seventeenth century at war with the Netherlands, Scotland, Ireland and itself. The country recovered quickly from the tyranny of Cromwell’s Commonwealth; the arrival of King William III from the Netherlands in 1689 brought peace with the Netherlands but still more wars in Europe, this time with France. In the second half of the seventeenth century, England lagged behind some of northern Europe, and most notably the Netherlands, in the sophistication of its financial systems. King William imported Dutch practices in the raising of long-term government funding, and his costly wars had much use for them.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See Hacking (1975) Chapter 1 for a survey of ancient probabilistic thinking and a discussion of what may have limited it.
- 2.
A total of ten can be produced by six distinct combinations: 6, 3, 1; 6, 2, 2; 5, 3, 2; 5, 4, 1; 4, 4, 2; 4, 3, 3. A total of nine can be produced by the six distinct combinations: 6, 2, 1; 5, 3, 1; 5, 2, 2; 4, 4, 1; 4, 3, 2; 3, 3, 3.
- 3.
Huygens (1657).
- 4.
See, for example, Section 1.3, Daston (1988) for a scholarly discussion of the legal doctrine of equity and its influence on the development of mathematical expectation.
- 5.
Chapter II, Todhunter (1865).
- 6.
Cox et al. (1979).
- 7.
Francis (1853).
- 8.
Infants that have not yet been christened.
- 9.
The mortality rates implied by Graunt’s survival table increase after age 56, but this arises due to rounding of the number of remaining survivors from a pool that begins with the arbitrary total of 100 (‘for men do not die in exact proportions nor in fractions’) rather than by explicit design.
- 10.
- 11.
See Homer and Sylla (1996), p. 112.
- 12.
De Witt (1671).
- 13.
1 − 28/30 = 6.7 %; and 1 − 126/128 = 1.6 %.
- 14.
Halley (1693).
- 15.
Hacking (1975), p. 113.
- 16.
Price (1772), Essay IV.
- 17.
Hacking (1975), Chapter 13, p. 111.
- 18.
Ogborn (1953), Phillips in Discussion, p. 196.
- 19.
Chapter IX, Homer and Sylla (1996).
- 20.
Homer and Sylla (1996) p. 127.
- 21.
Francis (1853), Chapter 3, p. 55.
- 22.
Leeson (1968), p. 1.
- 23.
Leeson (1968), p. 1.
- 24.
Daston (1988), p. 139.
- 25.
Chapter IV, Walford (1868).
- 26.
Francis (1853), p. 59.
- 27.
- 28.
Price (1772), p. 105.
- 29.
Stigler (1986).
- 30.
Todhunter (1865).
- 31.
De Moivre (1718).
- 32.
De Moivre (1724).
- 33.
Stigler (1986), p. 84.
- 34.
De Moivre (1724).
- 35.
Chapter IX, Francis (1853).
- 36.
Part A of Supple (1970) provides an excellent account of the establishment and early growth of Royal Exchange Assurance.
- 37.
See, for example, Section 3.4.2, Daston (1988).
- 38.
Bernoulli (1738).
- 39.
De Morgan (1838), Chapter V, p. 101.
- 40.
Samuelson (1960).
References
Bernoulli, Daniel (1738), ‘Specimen theoriae novae de mensura sortis’, Commentarii academiae scientarum imperialis Petropolitanae 5.
Cox, J.C., S.A. Ross and M. Rubinstein (1979), ‘Option Pricing: A Simplified Approach’, Journal of Financial Economics, Vol. 7, No. 3.
Daston, Lorraine (1988), Classical Probability in the Enlightenment. Princeton University Press.
De Moivre, Abraham (1718), Doctrine of Chances.
De Moivre, Abraham (1724), Annuities on Lives.
De Morgan, Augustus (1838), An Essay on Probabilities and On Their Applications to Life Contingencies and Insurance Offices. Longman, Orme, Brown, Green & Longmans.
De Wittt, Johan (1671), ‘In A Series of Letters to the States-General’, In R.G. Barnwell and F. Hendricks, A Sketch of the Life and Times of John De Witt, Grand Pensionary of Holland. New York, 1856.
Francis, John (1853), Annals, Anecdotes and Legends; A Chronicle of Life Assurance. Longman, Brown, Green & Longmans.
Hacking, Ian (1975), The Emergence of Probability. Cambridge University Press.
Halley, Edmond (1693), An Estimate of the Degrees of the Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslau, with an Attempt to ascertain the Price of Annuities upon Lives.
Homer, Sidney and Richard Sylla (1996), A History of Interest Rates, Third Edition Revised. Rutgers University Press.
Huygens, C. (1657), Ratiociniis in aleae ludo.
Leeson, Francis (1968), A Guide to the Records of the British State Tontines and Life Annuities of the 17th and 18th Centuries. Pinhorns.
Ogborn, M.E. (1953), ‘On the Nature of the Function Expressive of the Law of Human Mortality’. Journal of the Institute of Actuaries, Vol. 79, pp. 170–212.
Price, Richard (1772), Observations on Reversionary Payments; on Schemes for Providing Annuities for Widows, and for Persons in Old Age; To Which Are Added Four Essays. T. Cadfll.
Samuelson, P.A. (1960), ‘The St. Petersburg Paradox as a Divergent Double Limit’. International Economic Review, Vol. 1, No. 1.
Stigler, Stephen M. (1986), The History of Statistics. Belknap Harvard.
Supple, Barry (1970), The Royal Exchange Assurance: A History of British Insurance 1720–1970. Cambridge University Press.
Todhunter, Isaac (1865), History of the Mathematical Theory of Probability From the Time of Pascal to That of Laplace. London and Cambridge.
Walford, Cornelius (1868), The Insurance Guide and Hand-Book. Charles and Edwin Layton.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 The Author(s)
About this chapter
Cite this chapter
Turnbull, C. (2017). Probability and Life Contingencies, 1650–1750: The First One Hundred Years. In: A History of British Actuarial Thought. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-33183-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-33183-6_1
Published:
Publisher Name: Palgrave Macmillan, Cham
Print ISBN: 978-3-319-33182-9
Online ISBN: 978-3-319-33183-6
eBook Packages: Economics and FinanceEconomics and Finance (R0)