Types of Decrements

Typical life insurance policies include the following types of decrements:

1. Survival

2. Death

3. Lapse

4. Maturity

5. Critical Illness

Survival is also known as the number of policies inforce. It is the expected number of policies survived at the end of the measurement period (typically 1 year or 1 month).

Death is the number of policies that died within the measurement period. The death rate is often denoted by the symbol qx, which is the annual death rate of policy.

Most of countries will perform its population census regularly and create its own mortality table. For example, in the United States, the mortality table that the industry commonly adopted is called "CSO 2001". 

Lapse is the number of policies that quit the contract within the measurement period. Lapse shall include both surrenders (act voluntarily by the policyholder) and lapses (terminated by insurers due to various reason, for example missing premium), but in practice we called it "lapses" which include both situation. The lapse rate is often denoted by the symbol wx, which is the annual lapse rate of policy.

Lapse is very dependent on product features and customer segments, hence lapse rate often varies significantly by many dimensions such as policy year, product groups, channels, contract size, etc.

Maturity is the number of policies that survived until the end of the contract. For example, with an initial 10,000 policies inforce, 800 died and 5,200 lapsed, the number of maturity is then 10,000 - 800 - 5,200 = 4,000. Maturity is not measured by "maturity rate" and simply equal to the number of policies inforce at the end of the contract term.

Critical Illness is the number of policies that suffered from some predefined critical illness (eg: Heart Attack, Stroke, etc.) within the measurement period. While the policyholder may not die due to these diseases, the insurance contract will typically pay out a substantial benefit to the policyholder and terminates the contract afterwards. The critical illness rate is often denoted by the symbol ix, which is the annual morbidity rate of policy.

A demonstration spreadsheet showing mortality table, lapse table and basic contract information can be downloaded here:

https://drive.google.com/file/d/0B4OirwHLcmE1UkRaSWtLS2RvTHM/view?usp=sharing

There are many other possible decrements that can be added to decrement model, and tricks to play with if one wished to measure "non-terminated transition states". We will leave these advanced topic to the chapter on "Generalized Decrement Model".