Markov (Set) chains application to predict mortality rates using extended Milevsky–Promislov generalized mortality models

The mortality rates ( $ \mu _{x,t} $ μx,t) measure the frequency of deaths in a fixed: population and time interval. The ability to model and forecast $ \mu _{x,t} $ μx,t allows determining, among others, fundamental characteristics of life expectancy tables, e.g. used to determine the amount of premium in life insurance, adequate to the risk of death. The article proposes a new method of modelling and forecasting $ \mu _{x,t} $ μx,t, using the class of stochastic Milevsky–Promislov switch models with excitations. The excitations are modelled by second, fourth and sixth order polynomials of outputs from the non-Gaussian Linear Scalar Filter (nGLSF) model and taking into account the Markov (Set) chain. The Markov (Set) chain state space is defined based on even orders of the nGLSF polynomial. The model order determines the theoretical values of the death rates. The obtained results usually provide a more precise forecast of the mortality rates than the commonly used Lee–Carter model.