ON THE VALUE OF REVERSIONS. 221 



allow that advantage to the insured, if he afterwards 

 desire to sell his policy to the office itself. I am not 

 aware of the exact rule which is followed by the offices 

 in this respect, except in one or two cases, in which 

 the plan is, or was, to follow their own tables, with a 

 certain deduction from the result, and to give the dif- 

 ference to an insured party who desired to sell his 

 policy. This is well enough in the case of offices which 

 return profits ; but if such a rule be followed by those 

 which do not, it may amount to a contradiction of their 

 profession in the case of the sale of policies; and may 

 become in effect an allowance of that share in the profits 

 to those who desire to leave the office, which they re- 

 fuse to grant to those who continue. To prevent such 

 a result, I believe the offices who would be liable to it, 

 make a large deduction from the value of policies, as in- 

 dicated by their tables. 



All the preceding rules apply to any given status as 

 well as to a given life. Thus, to effect an insurance on 

 the survivor of two lives, the present value and the 

 premium (payable as long as either, is alive) are to be 

 found by using |A + |B - |AB for the value of the an- 

 nuity, instead of |A. I now proceed to some simple 

 cases of insurance, where the payment on one party's 

 death is made conditional upon another party being alive 

 to receive it. 



The symbol A| (IB) denotes the value of an annuity 

 upon the joint continuance of one year and the life of B, 

 payment being made at the end of the year in which A 

 dies. It is therefore necessary that B should be alive 

 at the end of the year in which A dies. But in the 

 usual conditions of contingent insurances, it is sufficient 

 that B should be alive at the moment in which A dies. 



Let this be expressed by A] IB ; it is then evident that 



A | IB is greater than A| IB. The following preliminary 

 considerations will be necessary. 



PROBLEM. Required the value of an annuity on the 

 joint lives of A and B, to be paid at every end of a 

 year at which B shall be alive, provided A were alive 



