Skip to main content
Erschienen in:
Buchtitelbild

2017 | OriginalPaper | Buchkapitel

1. Probability and Life Contingencies, 1650–1750: The First One Hundred Years

verfasst von : Craig Turnbull

Erschienen in: A History of British Actuarial Thought

Verlag: Springer International Publishing

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
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
Francis (1853), Chapter 1, p. 11, Hacking (1975), Chapter 12, p. 106.
 
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
For example, see Daston (1988) Section 3.4, Hacking (1975), p. 113.
 
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).
 
Literatur
Zurück zum Zitat Bernoulli, Daniel (1738), ‘Specimen theoriae novae de mensura sortis’, Commentarii academiae scientarum imperialis Petropolitanae 5. Bernoulli, Daniel (1738), ‘Specimen theoriae novae de mensura sortis’, Commentarii academiae scientarum imperialis Petropolitanae 5.
Zurück zum Zitat Cox, J.C., S.A. Ross and M. Rubinstein (1979), ‘Option Pricing: A Simplified Approach’, Journal of Financial Economics, Vol. 7, No. 3. Cox, J.C., S.A. Ross and M. Rubinstein (1979), ‘Option Pricing: A Simplified Approach’, Journal of Financial Economics, Vol. 7, No. 3.
Zurück zum Zitat Daston, Lorraine (1988), Classical Probability in the Enlightenment. Princeton University Press. Daston, Lorraine (1988), Classical Probability in the Enlightenment. Princeton University Press.
Zurück zum Zitat De Moivre, Abraham (1718), Doctrine of Chances. De Moivre, Abraham (1718), Doctrine of Chances.
Zurück zum Zitat De Moivre, Abraham (1724), Annuities on Lives. De Moivre, Abraham (1724), Annuities on Lives.
Zurück zum Zitat De Morgan, Augustus (1838), An Essay on Probabilities and On Their Applications to Life Contingencies and Insurance Offices. Longman, Orme, Brown, Green & Longmans. De Morgan, Augustus (1838), An Essay on Probabilities and On Their Applications to Life Contingencies and Insurance Offices. Longman, Orme, Brown, Green & Longmans.
Zurück zum Zitat 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. 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.
Zurück zum Zitat Francis, John (1853), Annals, Anecdotes and Legends; A Chronicle of Life Assurance. Longman, Brown, Green & Longmans. Francis, John (1853), Annals, Anecdotes and Legends; A Chronicle of Life Assurance. Longman, Brown, Green & Longmans.
Zurück zum Zitat Hacking, Ian (1975), The Emergence of Probability. Cambridge University Press. Hacking, Ian (1975), The Emergence of Probability. Cambridge University Press.
Zurück zum Zitat 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. 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.
Zurück zum Zitat Homer, Sidney and Richard Sylla (1996), A History of Interest Rates, Third Edition Revised. Rutgers University Press. Homer, Sidney and Richard Sylla (1996), A History of Interest Rates, Third Edition Revised. Rutgers University Press.
Zurück zum Zitat Huygens, C. (1657), Ratiociniis in aleae ludo. Huygens, C. (1657), Ratiociniis in aleae ludo.
Zurück zum Zitat Leeson, Francis (1968), A Guide to the Records of the British State Tontines and Life Annuities of the 17th and 18th Centuries. Pinhorns. Leeson, Francis (1968), A Guide to the Records of the British State Tontines and Life Annuities of the 17th and 18th Centuries. Pinhorns.
Zurück zum Zitat 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.CrossRef 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.CrossRef
Zurück zum Zitat 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. 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.
Zurück zum Zitat Samuelson, P.A. (1960), ‘The St. Petersburg Paradox as a Divergent Double Limit’. International Economic Review, Vol. 1, No. 1. Samuelson, P.A. (1960), ‘The St. Petersburg Paradox as a Divergent Double Limit’. International Economic Review, Vol. 1, No. 1.
Zurück zum Zitat Stigler, Stephen M. (1986), The History of Statistics. Belknap Harvard. Stigler, Stephen M. (1986), The History of Statistics. Belknap Harvard.
Zurück zum Zitat Supple, Barry (1970), The Royal Exchange Assurance: A History of British Insurance 1720–1970. Cambridge University Press. Supple, Barry (1970), The Royal Exchange Assurance: A History of British Insurance 1720–1970. Cambridge University Press.
Zurück zum Zitat Todhunter, Isaac (1865), History of the Mathematical Theory of Probability From the Time of Pascal to That of Laplace. London and Cambridge. Todhunter, Isaac (1865), History of the Mathematical Theory of Probability From the Time of Pascal to That of Laplace. London and Cambridge.
Zurück zum Zitat Walford, Cornelius (1868), The Insurance Guide and Hand-Book. Charles and Edwin Layton. Walford, Cornelius (1868), The Insurance Guide and Hand-Book. Charles and Edwin Layton.
Metadaten
Titel
Probability and Life Contingencies, 1650–1750: The First One Hundred Years
verfasst von
Craig Turnbull
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-33183-6_1