Estimating Indonesian Complete Life Table and Fair Annual Pure Premium Range from Abridged Life Table with Bayesian Method and Bootstrapping

Christian Evan Chandra (1), Sarini Abdullah (2), Sindy Devila (3)
(1) Department of Mathematics, University of Indonesia, Kampus Baru UI Depok, 16424, Indonesia
(2) Department of Mathematics, University of Indonesia, Kampus Baru UI Depok, 16424, Indonesia
(3) Department of Mathematics, University of Indonesia, Kampus Baru UI Depok, 16424, Indonesia
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Chandra, Christian Evan, et al. “Estimating Indonesian Complete Life Table and Fair Annual Pure Premium Range from Abridged Life Table With Bayesian Method and Bootstrapping”. International Journal on Advanced Science, Engineering and Information Technology, vol. 12, no. 6, Dec. 2022, pp. 2226-3, doi:10.18517/ijaseit.12.6.14947.
Several Indonesian life insurance companies recently faced financial problems due to inadequate pricing and idealistic investment expectation. Growing market and insurtech implementation might lead to worse conditions in the future. The current mortality table and investment return assumption are too ideal, so more conservative assumptions are required to get a more reasonable annual pure premium range. This research estimated complete life tables from abridged life tables by truncated Heligman-Pollard and Makeham model, when a lognormal stochastic process estimated annual investment return. Parameters for mortality models and return distribution are estimated using Bayesian method with Metropolis-Hasting’s algorithm. Data from the abridged life table was bootstrapped due to insufficient number for statistical parametric modeling. Good accuracy for estimated abridged mortality rates was reached by referring to the Mean Absolute Percentage Error (MAPE) metric for both males and females, also for the young ages group (new-born to twenty-nine years old) and old ages group (thirty to eighty-four years old). The parameters were satisfactory to estimate the complete life table and extrapolate annual mortality rates calculation until age ninety-nine. A log-normal distribution was found to fit the monthly inflation rates satisfactorily. Assuming that investment return is close to the inflation rates, the annual investment return is anticipated for both profitable and losing situations. Therefore, insurance companies can win the customers’ decisions without compromising their financial stability.

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