On contemporary mortality models for actuarial use II: principles

Abstract We reprise some common statistical models for actuarial mortality analysis using grouped counts. We then discuss the benefits of building mortality models from the most elementary items. This has two facets. First, models are better based on the mortality of individuals, rather than groups. Second, models are better defined in continuous time, rather than over fixed intervals like a year. We show how Poisson-like likelihoods at the “macro” level are built up by product integration of sequences of infinitesimal Bernoulli trials at the “micro” level. Observed data is represented through a stochastic mortality hazard rate, and counting processes provide the natural notation for left-truncated and right-censored actuarial data, individual or age-grouped. Together these explain the “pseudo-Poisson” behaviour of survival model likelihoods.