CISC 121 Lecture Notes - Lecture 8: Equivalence Principle, Life Annuity, Life Insurance

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CISC 121 Full Course Notes
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CISC 121 Full Course Notes
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Typically, life insurance benefits will not be paid for with a net single premium but rather by a series of payments in the form of a life annuity. Deferred life annuities may also be purchased in this manner. To set the price, we must first introduce the loss random variable, l. L = present value (benefits) present value (premiums) The method we will almost exclusively use to solve for the premium is called the equivalence principle. E[l] = e[present value(benefits)] e[present value (premiums)] When using the equivalence principle, the premium can simply be denoted: in rare cases where the equivalence principle is not used, the symbol p will be used to represent the premium. We will only deal with premiums paid on an annual basis or net single premiums. Therefore, if you are using the equivalence principle, there is no accumulation type benefit and you know any two of e[z], e[y] and p, you can easily find the third.

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