excans:4121c932c4

Answer: A

The contribution from Life 1 is [math]{ }_{20} p_{70}[/math]. With Gompertz and the selected parameters, the contribution is [math]{ }_{20} p_{70}=\exp \left[-\frac{B}{\ln c} c^{70}\left(c^{20}-1\right)\right]=\exp \left[-\frac{0.000003}{\ln 1.1} 1.1^{70}\left(1.1^{20}-1\right)\right]=0.86730[/math].

The contribution from Life 2 is [math]{ }_{19} p_{70}-{ }_{20} p_{70}[/math]. The contribution is

[[math]] \begin{aligned} & { }_{19} p_{70}-{ }_{20} p_{70}=\exp \left[-\frac{B}{\ln c} c^{70}\left(c^{19}-1\right)\right]-0.86730=\exp \left[-\frac{0.000003}{\ln 1.1} 1.1^{70}\left(1.1^{19}-1\right)\right]-0.86730 \\ & =0.88058-0.86730=0.01328 \end{aligned} [[/math]]

The contribution to the likelihood is [math]0.86730(0.01328)=0.01152[/math].

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.