Many actuaries worldwide use Systematic Mortality Risk (SMR) to value actuarial prod-
ucts 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 modifi-
cations of the classical SMR models used in those countries with limited data availability.
This study aims at modelling SMR stochastically under the collateral data environment
such as Sub-Saharan African countries like Kenya and then apply it in the current actuar-
ial 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-time-
cohort. After testing SMR models on the Kenyan data to assess their behaviours, we
incorporate the Bühlmann Credibility Approach with random coefficients in modeling.
The randomness of the classical SMR models is 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 solves data paucity during the SMR model fitting
and forecasting. The forecasting performances of the SMR models are done under DNN
and, compared with those from conventional models, show powerful empirical illustra-
tions in their precision levels. Numerical results show 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 offers much more
accurate valuations when compared to those under classical models. The study’s find-
ings 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.