\( \newcommand{\sfrac}{l} \newcommand{\ssfrac}{\hat{\sfrac}} \newcommand{\spread}{\delta} \)

Relative Spread

Given a set of age nodes \(0=x_0,x_1,\ldots,x_n\) and survival fractions \(1=\sfrac(x_0),\sfrac(x_1),\dots,\sfrac(x_n)\) the force of mortality over the interval \([x_i,x_{i+1})\) is a constant relative spread \(\spread_i\) relative to the force for a standard curve \(\ssfrac(x)\). \begin{equation} \sfrac(x)=\sfrac(x_i) \left(\frac{\ssfrac(x)}{\ssfrac(x_i)}\right)^{1+\spread_i},\quad x\in [x_i,x_{i+1}) \end{equation} See Kostaki (2000) for details. The build method property must be of the form REL_SPREAD:SMortHandle where SMortHandle is the name of the standard mortality object enclosed in quotes.