THE MATHEMATICS OF LIFE INSURANCE' 



By S. Epsteen 



§ I. Introduction 



Just as everybody eats bread without knowing its chemical composi- 

 tion, so everybody uses insurance without understanding its nature. 

 Insurance is a guarantee of indemnity; its object is to replace money or 

 other property that is lost. The theory of the system is this: Many 

 people who are subject to a common danger of financial loss agree to 

 pool their expected losses by providing in advance, by general contribu- 

 tion, a fund from which those who actually suffer loss may be indemnified. 



If a man insures his house for exactly what it is worth, say $5,000, 

 and pays $50 per year, and the house burns, he receives $5,000. Thus 

 he is in almost as good a position financially as before, having lost only 

 the amount of the premium — $50. In this respect, however, he is in 

 exactly the same position as every other man insured for a like amount 

 on equally valuable property and at the same time — each of them has lost 

 exactly $50 and each has $5,000 less $50. The fact that one man has 

 $5,000 in cash and the others each have $5,000 worth of house does not 

 affect the comparison. It is thus seen that insurance is a co-operative 

 scheme whereby each member of the community pockets a small loss 

 in place of one member sustaining a severe loss. The insurance com- 

 pany acts as an intermediary in distributing this loss. 



Life insurance does not insure life in quite the same sense that fire 

 insurance insures a house or marine insurance a ship. Should the 

 house burn or the ship sink the insurance company can (and sometimes 

 does) substitute another for it. But one cannot substitute a new life for 

 the one terminated. In life insurance one insures the product of the 

 effort which a man exerts when alive (and which he cannot exert when 

 dead), and not hfe itself. 



' Read before the University of Colorado Scientific Society, January 29, 1906. In preparing §1 I have 

 followed Campbell's Insurance and Crime, Introduction, and in §3, Educational Leaflets No. 2, issued by 

 the Mutual Life Insurance Co. of New York. 



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