Sessional meeting: Contemporary mortality models for actuarial use

Thu 24 Oct 2024 -
17:00 - 18:00 (BST)

A joint presentation of both papers by Prof Angus S MacDonald and Dr Stephen J Richards.

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