280 PROCEEDINGS OF SECTION A. 



8.— THE APPLICATION OF MATHEMATICS TO 

 ACTUARIAL SCIENCE. 



By JOSEPH J. STUCKEY, M.A. 

 [Abstract.] 



I am very glad that the work of an actuary can now, with any 

 degree of fairness, be classed as a science, and that the certainties 

 of mathematics are applicable to this branch of science, although 

 it deals with such uncertainties as the duration of individual life or 

 of the sickness which anyone will experience during life, the pro- 

 bability that a bachelor of a certain age will marry, the probability 

 of issue, of fires, of accident, of marine disaster, and many others. 



The method which I propose to adopt in this paper is to take, 

 first, the most advanced branch of actuarial science, and give the 

 application of mathematics to the various stages in chronological 

 order. This, it is hoped, will be satisfactory, although it takes the 

 various branches of mathematics in very much the inverse order of 

 difficulty. 



Life msurance is the most advanced branch of actuarial science, 

 but is still pushing on to greater and greater scientific exacti- 

 tude. It is the comi^oimd growth, first, of our commercial 

 necessities, excited by a love of speculation, and, later, of our 

 progressive civilisation. For the former, rough and ready means 

 of estimation were resorted to ; for the latter, a long and elaborate 

 course of progressive investigation was needed. The development 

 has taken some three or foiu- centuries, and has had three phases 

 — The experimental period, the speculative period, and the period 

 of scientific exactitude. 



It was, we are told, 1721 with which this third period began, 

 though the early specimens of life policies of this period are too 

 like the present fire and marine to have much claim to be scientific. 

 They were for one year at 5 per cent., irrespective of age, and 

 seem to have been taken from the then rate of insurance on ships. 

 This period of scientific exactitude is said to have culminated in 

 1769, with the advent of the Northampton Table of Mortality, and 

 the coincident work of Dr. Price on " Reversionary Payments, &c." 



I imagine I can hardly claim that any jjreat use is made of 

 mathematics in the collection of the statistics of life, age, and death, 

 but I may remark that the imperfection and incompleteness of the 

 statistics so collected has required of the actuary and mathematician 

 two things, at least-^the supervision of ; the collection of new sta- 

 tistics, arid the adjustment and graduation of the tables of mortality 

 obtained from those already collected; The bills of mortality, the 

 registers oi birth, life, and death, were made for other purposes; but 

 it was early seen that the application of the principles of probability 

 to these bills woxdd enable them to furnish the expectations of life 

 and the values of annuities, assurances, and premiums, at any 

 selected rate of interest. They were for a long time used in their 



