On contemporary mortality models for actuarial use: practice
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: 

• reflecting the reality of data produced by everyday business practices 
• modelling rapid changes in risk 
• modelling time- and duration-varying risk 
• competing risks 
• data-quality checking 
• management information 

Specific examples are given where continuous-time models are more useful in practice than discrete-time models. 

On contemporary mortality models for actuarial use: principles 
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.

Speakers Prof Angus S Macdonald and Dr Stephen J Richards