
151
can apply the proposition (12.6) and see that in the case of compound-
ing c(t) and p(t) the ratio p/c is larger than in the case of level cover
with constant c and p. This does not imply, of course, that the contract
in the compounding case is “more expensive” – in both contracts the
expected values of what the policyholder and insurance company pay
are equal; but in the case of the compounded amounts larger sums are
changing hands.
Group life insurance. Consider a group of k persons of ages
x
1
,x
2
,... ,x
k
entering into a joint life insurance contract with an insur-
ance company. Let the distribution functions of the remaining lifetimes
T
1
−x
1
,T
2
−x