Stochastic Modelling of Systematicmortality Risk Under Collateral Data and Its Applications

Abstract

Many actuaries worldwide use Systematic Mortality Risk (SMR) to value actuarial products such as annuities and assurances sold to policyholders. Data availability plays an essential role in ascertaining the SMR models’ accuracy, and it varies from one country to another. Incorrect stochastic modeling of SMR models due to paucity of data has been a problem for many Sub-Saharan African countries such as Kenya, thus prompting modifications of the classical SMR models used in those countries with limited data availability. This study aimed at modelling SMR stochastically under the collateral data environment such as Sub-Saharan African countries like Kenya and then apply it in the current actuarial valuations. This thesis has formulated novel stochastic mortality risk models under the collateral data setup. Kenya population data is preferably integrated into the commonly applied stochastic mortality risk models under a 3-factor unitary framework of age-timecohort. After testing SMR models on the Kenyan data to assess their behaviours, we incorporate the Buhlmann Credibility Approach with random coefficients in modeling. The randomness of the classical SMR models wass modeled as NIG distribution instead of Normal distribution due to data paucity in Kenya (use of collateral data environment). The Deep Neural Network (DNN) technique solved data paucity during the SMR model fitting and forecasting. The forecasting performances of the SMR models were done under DNN and, compared with those from conventional models, show powerful empirical illustrations in their precision levels. Numerical results showed that SMR models become more accurate under collateral data after incorporating the BCA with NIG assumptions. The Actuarial valuation of annuities and assurances using the new SMR offered much more accurate valuations when compared to those under classical models. The study’s findings should help regulators such as IRA and RBA make policy documents that protect all stakeholders in Kenya’s insurance, social protection firms, and pension sectors. For areas for further research, one can use the BCA approach for Sub-Saharan African countries with similar demographic characteristics and Hierarchical BCA in SMR modeling.