This research looks at the scheme proposed in the paper Pollard (1970). The scheme
is based on a two-state model for the analysis of one-year mortality, but the results
are also valid for the probabilities related to other types of insurance events such as
disablement and accidents. Pollard (1970) proposed a scheme involving calculation of
expected value, and the variance of the number of deaths within a given population,
under different settings starting from the simplest binomial case, through more general
cases where uncertainty is allowed for and more risk classes are considered. In all the
settings, the individual events are independent or conditionally independent.
The purpose of this study is to extend the Pollard's original scheme into time-discrete
models with more states (active-invalid-dead) together with further investigation into
multi-year time horizon. Additionally, hypotheses for real-valued individual frailty are
assumed in the models. As a baseline probabilistic structure, we have adopted a traditional
three-state model in a Markov context.
Our outputs of interest are based on the probability distributions of the annual payouts
for term insurance policies providing lump sum benefits both in case of death and in
case of permanent disability. The analysis of the probability distributions allows us to
assess the risk profile of the insurance portfolio, and thus to suggest appropriate actions
in terms of premiums and capital allocation. In this regards, we adopt the percentile
principle.
