Mortality risk modelling using the feller process.

Abstract

In the present century, modelling of mortality risk has become a prerequisite consideration in the insurance industry, especially in product pricing and claims reserving. Actuaries and statisticians have developed various methods for modelling mortality risks for use in insurance product pricing and claim reserving. However, there is room for more improved methods in mortality risk modelling. The current paper was designed to model mortality rates using a ine stochastic process, namely the Feller process. The Feller model was derived from first principle by a simply modification of the CIR process in order to eliminate the mean-reversion element. The Kenyan 2010 mortality rates for both male and female population were used to fit the derived Feller process by fi ing the data to the model. The process provided parameters estimates of the fi ed Feller model. The models were then tested for their goodness of fit and parameters profiled. The empirical analysis provided good and stable parameter estimates for both the female and male model models. The goodness of fit test also confirmed that the models perfectly fi ed the observed mortality rates data. The results of the empirical analysis confirmed that the Feller process provides a good avenue for modelling mortality rates for both female and male populations. The model is easy to implement in the calculation of the mortality rates since only the time element is needed – the parameters have been estimated. The model can be used in actuarial practice for insurance product pricing and claim reserving processes.