12.4 Approximations for large data sets
12.4.1 Introduction
The discussion in this section is motivated by the circumstances that accompany the determination of a model for the time to death (or other decrement) for use in pricing, reserving, or funding insurance programs. The particular circumstances are:
Values of the survival function are required only at discrete values, normally integral ages measured in years.
A large volume of data has been collected over a fixed time period, with most observations truncated, censored, or both.
No parametric distribution is available that provides an adequate model given the volume of available data.
These circumstances typically apply when an insurance company (or a group of insurance companies) conduct a mortality study based on the historical experience of a very large portfolio of life insurance policies. (For the remainder of this section we shall refer only to mortality. The results apply equally to the study of other decrements such as disablement or surrender.)
The typical mortality table is essentially a distribution function or a survival function with values presented only at integral ages. While there are parametric models ...
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