A comparison of Lee-Carter and Cairns-Blake-Dowd stochastic mortality model

摘要

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 Lee-Carter and Cairns-Blake-Dowd 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. In this paper we propose using the CBD model as a longevity risk indicator. The indicator contains only two set of numbers, κ_t~(1) and κ_t~(2), each of which is readily interpretable and they together tell how mortality rates at different ages change with time. It has the new-data invariant property.