Actuarial reserve

An actuarial reserve is a liability 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 is the sum of the actuarial reserves for every individual policy. Regulated insurers are required to keep offsetting assets to pay off this future liability.

The loss random variable is the starting point in the determination of any type of actuarial reserve calculation. Define ${\displaystyle K(x)}$ to be the future state lifetime random variable of a person aged x. Then, for a death benefit of one dollar and premium ${\displaystyle P}$, the loss random variable, ${\displaystyle L}$, can be written in actuarial notation as a function of ${\displaystyle K(x)}$

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