multiple-decrement models

Ordinary life tables track just one way to leave the group: death. But real populations of policyholders or employees can exit for several distinct reasons at once. A worker in a pension scheme might leave by retiring, resigning, becoming disabled, or dying — and once they leave by any one of these, they are no longer at risk of the others. A multiple-decrement model is a survival model with several competing exits (decrements) running in parallel.

The new ingredient is that each cause has its own intensity, and they compete. The rate of leaving by cause j at age x is a force of decrement, and the total force is just the sum of all causes. Because someone who retires this year can no longer resign or die-in-service this year, the observed (dependent) probability of each exit is lower than the rate that cause would produce on its own. So actuaries distinguish dependent decrement rates (what actually happens when all causes are present) from independent rates (what one cause would do if it acted alone). A multiple-decrement table tabulates, for an opening cohort, how many leave each year by each cause.

These models are everywhere money depends on why people leave, not just whether: pension funding (retirement versus withdrawal versus death pay different benefits), disability insurance, lapse-supported life products, and employee-benefit valuations. A frequent pitfall is forgetting the competition between causes — for instance, assuming you can lower the mortality decrement without affecting the others, when in fact removing one cause leaves more lives exposed to the rest.