Angus Macdonald
Emeritus Professor in the School of Mathematical and Computer Sciences at Heriot-Watt University
Articles written by Angus Macdonald
Introducing the Product Integral
Of all the actuary's standard formulae derived from the life table, none is more important in survival modelling than:
\[{}_tp_x = \exp\left(-\int_0^t\mu_{s+s}ds\right).\qquad(1)\]
Everything points to Poisson
One recurring theme in our forthcoming book, Modelling Mortality with Actuarial Applications, is the all-pervading role of likelihoods that suggest the lurking presence of a Poisson distribution. A popular assumption in modelling hazard rates is that the number of deaths observed at any given age is a Poisson random variable, so perhaps that might explain it?