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Fundamentals of Actuarial Mathematics, 3rd Edition by S. David Promislow

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9 Select mortality

9.1 Introduction

In this chapter we will discuss a refinement to our basic model. In previous chapters we assumed that for a sufficiently homogeneous group – North American male nonsmokers, for example – mortality rates are a function of attained age only. This may be a reasonably accurate assumption for the totality of people in this group, but it need not apply for certain subsets. An insurer, after all, is not interested in the mortality of the general population, but only the subset of those who buy policies. Observed data show that for purchasers of life insurance, mortality depends not only on age, but on duration since the policy was purchased. To see why this should be true, let us compare two people both age 60, alike in all respects except that A just recently purchased an insurance policy, and B purchased a policy 1 year ago at age 59. During the next year, we would expect that A will have a higher probability of living to age 61 than B will. This arises from the fact that the insurer does not have to accept everyone who applies for a policy. Applicants can be requested to undergo medical exams, or to furnish information regarding their health, lifestyle and other factors, in order to verify that they are reasonable risks. Individual A has just been so certified. Individual B, on the other hand, was certified as a good risk 1 year ago, but this condition could have changed. B may have contracted a fatal disease, or taken up life-threatening habits. ...

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