By Browers Gerber Hickman
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Extra resources for Actuarial Mathematic, Second Edition
Since insurance is only offered to individuals of good health (sometimes only after a medical test), it is reasonable to expect that a person who has just bought insurance, will be of better health than a person who bought insurance several years ago, other factors (particularly age) being equal. This phenomenon is taken into account by select life tables. In a select life table, the probabilities of death are graded according to the age at entry. Thus q[x]+t is the one-year probability of death for (x + t) with x as entry age.
1. Note that m m independence between K and S implies independence between K and s(m). Furthermore, if S has a uniform distribution between 0 and 1, then s(m) has a discrete uniform distribution. Chapter 2. 5 Life Tables In the previous sections of this chapter we considered a person of age x. The probability distribution of his future lifetime can be constructed by adopting a suitable life table. A life table is essentially a table of one-year death probabilities qx' which completely defines the distribution of K.
The net single premium at age x is the expected value of a random variable defined as discounted sum insured in case of death, and discounted net single premium at age x + 1 in case of survival. 4) First the amount of Ax+l is reserved in any case (death or survival). In case of death an additional 1 - Ax+! is needed to cover the payment. ) qx. 6) L k=O so that the net single premium at age x is evidently the sum of the net single premiums of a series of one-year term insurances. 7) Thus the interest earned has a dual effect: On the one hand it increases the net single premium (from age x to age x + 1), and on the other it finances a fictitious one-year term insurance.