Thu 24 Oct 2024 - A joint presentation of both papers by Prof Angus S MacDonald and Dr Stephen J Richards.
Actuaries must model mortality to understand, manage, and price risk. Continuous-time methods offer considerable practical benefits to actuaries analysing portfolio mortality experience. This paper discusses 6 categories of advantage:
Specific examples are given where continuous-time models are more useful in practice than discrete-time models.
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 elemental items. This has 2 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 survival probabilities at the ‘macro’ level arise at the ‘micro’ level from a series of Bernoulli trials over infinitesimally small time periods. Using a multiplicative representation of the mortality hazard rate, we show how counting processes naturally represent left-truncated and right-censored actuarial data, individual or age-grouped. Together these explain the ‘pseudo-Poisson’ behaviour of survival model likelihoods.
Prof Angus S MacDonald and Dr Stephen J Richards