Modelling mortality by continuous benefit amount

Mortality levels vary by benefit amount, and a common simplification is to group by non-overlapping ranges of varying widths. However, this ignores the continuous nature of benefit amounts and leads to discretisation error, i.e. heterogeneity within benefit ranges and step jumps at range boundaries. Another drawback of discretisation is that fitted parameters are not easily extrapolated to values outside the range of the experience data. To address these shortcomings it is often better to model mortality continuously by benefit amount. In this paper we present a method of modelling mortality levels continuously by a financial covariate such as pension size. We split the task into (i) a transform function to address the presence of extreme benefit amounts in actuarial data sets, and (ii) a response function to model mortality. Using as few as two parameters, the method avoids discretisation error and extrapolates to amounts outside the range covered by the calibrating data set. We illustrate the method by applying it to seven international data sets of pensioners and annuitants.