Probability Patterns

Statistical Distribution

Insurance probability tables
Actuarial Tables - Mortality and Demographic Data from Actuary.com

Period Life Table

Updated June 27, 2006

http://www.ssa.gov/OACT/STATS/table4c6.html

Insurance applications

In order to price insurance products, and ensure the solvency of insurance companies through adequate reserves, actuaries must develop projections of future insured events (such as death, sickness, disability, etc.). To do this, actuaries develop mathematical models of the causes of these events, as well as the amount and timing of the events. They do this by studying the incidence and severity of these events in the recent past, developing expectations about how the drivers of these past events will change over time (for example, whether the increase in life expectancy that has been experienced by most generations over prior generations will continue) and, accordingly, develop an expectation for what the timing and amount of such events will be into the future. These expectations usually take the form of tables of percentages indicating the number of such events that will occur in a population, usually based on the age or other relevant characteristics of the population. More specifically, they may be referred to as mortality tables (if they provide rates of mortality, or death), morbidity tables (if they provide rates of disability and recovery), or by other names if they cover other decrements.

The invention of computers and the proliferation of data gathering about individuals has led to fundamental changes in the way actuarial tables are computed for different uses, and a variety of emerging methods factor a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk.

The mathematics

To give an indication of how life tables are used, here are a few sample calculations. These samples may not be obvious to someone who has never studied probability theory, but are intended to introduce new ideas to people who have some understanding of discrete probability theory.

$\,q_x$ : the probability that someone aged exactly $\,x$ will die before their $\,(x+1)$ ^th birthday
$\,p_x$ : the probability of surviving from age $\,x$ to age $\,(x+1)$