The classical mortality models such as the Cairns-Blake-Dowd (CBD), Lee-Carter (LC), Linear Regression (LR) models are used to model Systematic Mortality Risk (SMR) for many developed countries populations for actuarial product valuations. This research study aims at incorporating the Bühlmann credibility approach (BCA) to improve the SMR models to fit sub-Saharan African populations like Kenya. Since the Kenyan population does not exhibit the Gaussian properties used in modeling the classical error terms, we proposed using Normal Inverse Gaussian distribution to model these error terms instead of a Gaussian distribution. We model the error terms of the classical models (LC, CBD, and LR) as a Normal Inverse Gaussian (NIG) distribution through the Bühlmann credibility approach. This novel approach demonstrates an improved precision of the predicted SMR as shown by the values of MAPE and RMSE measures compared to those under classical mortality risk models. Ultimately, we have done actuarial valuations of annuities and assurances using our determined SMR, thus concluding that this BCA approach improves the accuracy of actuarial products sold in the Kenyan market.