Net Level Premium Reserves
Net level premium reserves, also called benefit reserves, only involve two cash flows and are used for some US GAAP reporting purposes. The valuation premium in an NLP reserve is a premium such that the value of the reserve at time zero is equal to zero. The net level premium reserve is found by taking the expected value of the loss random variable defined above. They can be formulated prospectively or retrospectively. The amount of prospective reserves at a point in time is derived by subtracting the actuarial present value of future valuation premiums from the actuarial present value of the future insurance benefits. Retrospective reserving subtracts accumulated value of benefits from accumulated value of valuation premiums as of a point in time. The two methods yield identical results (assuming bases are the same for both prospective and retrospective calculations).
As an example, consider a whole life insurance policy of one dollar issues on (x) with yearly premiums paid at the start of the year and death benefit paid at the end of the year. In actuarial notation, a benefit reserve is denoted as V. Our objective is to find the value of the net level premium reserve at time t. First we define the loss random variable at time zero for this policy. Hence
Then, taking expected values we have:
Setting the reserve equal to zero and solving for P yields:
For a whole life policy as defined above the premium is denoted as in actuarial notation. The NLP reserve at time t is the expected value of the loss random variable at time t given K(x)>t
- Where
Read more about this topic: Actuarial Reserves
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