M.Sc Thesis
M.Sc Student Wallach Miriam Nechama Modeling of Actuarial Life Tables Department of Mathematics Professor Emeritus Abraham Zaks

Abstract

A mortality table is a table giving for each age the number of survivors. That is, starting with l(0) simultaneous births, how many people are still alive at age x.   The crude data is  gathered from  censuses, processed and then tabulated.

Plotting these figures on a graph one gets an approximation of a curve. This curve is called a mortality curve

This paper attempts to produce a smooth function of reasonable complexity that preserves the shape of the mortality curve to within a tolerable deviation. We attempt to generate this smooth function using assorted modelling techniques. We also develop methods to apply the generated functions for use in standard actuarial calculations. The most significant example is to be able to easily and efficiently compute premiums for different types of insurances and pensions based on the continuous functions defined in the paper. As this method is continuous, this allows insurance/pension plans to be computed momently, that is they can be computed for any time interval and not only for  whole years.

This paper shows that using the continuous method and the functions generated the deviations from the published values are less than 10%. When premiums are computed, insurance companies assume the deviation to be at least this. Therefore, the continuous method can be used instead of the discrete method This paper also attempted to calculate future continuous life functions based on current functions. This was done using the least squares estimator and using assumptions on future life expectation