Chapter 7: Benefit Reserves
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7.1 Introduction to Benefit Reserves
In Chapter 6, we introduced the equivalence principle,
which assumes, at the time of policy issue,
[
]
[
]
Premiums of PVBenefits of PV EE
=
.
Example: A person bought a 100 whole life policy at age
40 with annual premiums of 1. At age 40 (time of issue):
[
]
[
]
Premiums Future of PVBenefits Future of PV EE
=
If the person is now age 99, then
[
]
[
]
Premiums Future of PVBenefits Future of PV EE
We denote
V
t
, the benefit reserve at time t:
[
]
[
]
Premiums Future of PVBenefits Future of PV EEV
t
−
=
Let the Prospective Loss at time t be:
Premiums Future of PVBenefits Future of PV
−
=
L
t
Thus, the Benefit Reserve at time t:
[
]
LEV
tt
=
In general:
V
t
= APV of future benefit – APV of future premiums
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