An insurer is modelling time to death of lives insured at age [math]x[/math] using the Kaplan-Meier estimator. You are given the following information.
(i) There were 100 policies in force at time 0
(ii) There were no new policies entering the study
(iii) At time 10.0, immediately after a death, there were 50 policies remaining in force
(iv) The Kaplan-Meier estimate of the survival function for death at time 10 is [math]\hat{S}(10.0)=0.92[/math]
(v) The next death after time 10.0 occurred when there was one death at time 10.8
(vi) During the period from time 10.0 to time 10.8 , a total of 10 policies terminated for reasons other than death
Calculate [math]\hat{S}(10.8)[/math], the Kaplan-Meier estimate of the survival function [math]S(10.8)[/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: A
[math]\hat{S}(10.8)=\hat{S}(10.0)\left(\frac{50-10-1}{50-10}\right)=0.897[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.