Lee-Carter family of stochastic mortality models

Abstract

Insurance companies are affected by many different kinds of risks. In the case of life insurance there are two main risks: the investment risk and the demographic risk. The latter can be split into insurance risk due to the random deviation of the number of deaths from its expected value, and longevity risk deriving from the improvement in mortality rates. Numbers of stochastic models have been developed to analyse the mortality improvement. This paper focuses on the family of Lee-Carter models. We use data on male’s deaths and exposures for the Czech Republic from the Human Mortality Database. We write the code associated with models in R. However, for actuaries the fitting of a model is usually only the first step and the main purpose is the forecasting of mortality.