The Loss Random Variable
The loss random variable is the starting point in the determination of any type of actuarial reserve calculation. Define to be the future state lifetime random variable of a person aged x. Then, for a death benefit of one dollar and premium, the loss random variable, can be written in actuarial notation as a function of
From this we can see that the present value of the loss to the insurance company now if the person dies in t years, is equal to the present value of the death benefit minus the present value of the premiums.
The loss random variable described above only defines the loss at issue. For K(x)>t, the loss random variable at time t can be defined as:
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