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The actuarial present value (APV) is the expected value of the present value of a contingent cash flow stream (i.e. a series of payments which may or may not be made). Actuarial present values are typically calculated for the benefit-payment or series of payments associated with life insurance and life annuities .
Actuarial notation is a shorthand method to allow actuaries to record mathematical formulas that deal with interest rates and life tables. Traditional notation uses a halo system , where symbols are placed as superscript or subscript before or after the main letter.
Both contractual liabilities, and future premiums in this calculation allow only for mortality and interest. The key with a net premium valuation is that the premiums being valued are theoretical measures - they make no reference to the actual premiums being charged by the insurer.
The opposite of discounting is compounding. Taking the example in reverse, it is the equivalent of investing 3,186.31 at t = 0 (the present value) at an interest rate of 10% compounded for 12 years, which results in a cash flow of 10,000 at t = 12 (the future value). The importance of NPV becomes clear in this instance.
Valuation of life annuities may be performed by calculating the actuarial present value of the future life contingent payments. Life tables are used to calculate the probability that the annuitant lives to each future payment period. Valuation of life annuities also depends on the timing of payments just as with annuities certain, however life ...
In insurance, an actuarial reserve is a reserve set aside for future insurance liabilities. It is generally equal to the actuarial present value of the future cash flows of a contingent event. In the insurance context an actuarial reserve is the present value of the future cash flows of an insurance policy and the total liability of the insurer ...
There are two algebraically equivalent approaches to calculating the Bornhuetter–Ferguson ultimate loss. In the first approach, undeveloped reported (or paid) losses are added directly to expected losses (based on an a priori loss ratio) multiplied by an estimated percent unreported.
Actuarial reinsurance premium calculation uses the similar mathematical tools as actuarial insurance premium. Nevertheless, Catastrophe modeling , Systematic risk or risk aggregation statistics tools are more important.