Information Matrix
Filter Information matrix
Posts feedIntroducing the Product Integral
Of all the actuary's standard formulae derived from the life table, none is more important in survival modelling than:
\[{}_tp_x = \exp\left(-\int_0^t\mu_{s+s}ds\right).\qquad(1)\]
From small steps to big results
In survival-model work there is a fundamental relationship between the \(t\)-year survival probability from age \(x\), \({}_tp_x\), and the force of mortality, \(\mu_x\):
\[{}_tp_x = \exp\left(-\int_0^t\mu_{x+s}ds\right).\qquad(1)\]