Mortality Table

A mortality table, also known as a life table, is a statistical tool that actuaries, insurers, and other professionals in the finance and healthcare sectors use to predict the life expectancy of a given population. By analyzing various factors such as age, gender, health, and other demographics, mortality tables help in understanding the probability of death at different ages. These tables are critical in fields like life insurance, pension planning, and risk management.

History and Development

The history of mortality tables dates back to the late 17th century when John Graunt, an English statistician, produced life tables using the death records of the inhabitants of London. Subsequent refinements were made by Edmund Halley, a renowned astronomer, who analyzed birth and death rates in the city of Breslau. These early studies laid the foundation for the more sophisticated tables used today.

Structure and Composition

Age-Specific Mortality Rates

Mortality tables are generally divided into age-specific intervals, typically categorized by each year of age. Each interval provides an estimate of the probability that a person of a particular age will die within the next year.

Survivorship Function

The survivorship function (denoted as l_x), shows the number of people who survive to a particular age, starting from an initial cohort of births (usually 100,000). This function helps in visualizing how many individuals from a particular cohort will live to various ages.

Probability of Dying

The probability of dying (denoted as q_x) between two ages is one of the key columns in a mortality table. It represents the likelihood that a person alive at age x will die before reaching age x+1.

Life Expectancy

Life expectancy values are often included, representing the average number of years remaining for an individual at a given age. It is derived from the survivorship function and provides crucial input for pension plans and annuities.

Types of Mortality Tables

Period Life Tables vs. Cohort Life Tables

• Period Life Tables: These tables use data from a specific time period and reflect the mortality experience of a population at that point in time.
• Cohort Life Tables (also known as Generation Life Tables): These analyze the mortality experience of a particular cohort from birth until death, offering a more longitudinal perspective.

Static vs. Dynamic Tables

• Static Mortality Tables: These tables don’t account for future improvements in mortality rates and are considered somewhat static in their predictions.
• Dynamic Mortality Tables: These account for expected changes in mortality rates over time, offering more sophisticated and accurate projections.

Actuarial Tables

These tables are specialized versions used in the insurance industry to price life insurance policies, annuities, and pensions. They incorporate various actuarial assumptions, such as interest rates and future mortality improvements.

Applications in Finance and Insurance

Life Insurance

Mortality tables are crucial in calculating life insurance premiums. By assessing the probability of death at different ages, insurers can determine the risk they are taking on and price their policies accordingly.

Pension Plans and Annuities

Life tables help in estimating the liabilities for pension plans by predicting the life expectancy of pensioners. This information is essential for determining how much money needs to be set aside to meet future pension obligations.

Healthcare and Social Security

Governments and policymakers use mortality tables to plan and allocate resources for public health programs and social security benefits. Estimations of life expectancy and death rates help in designing sustainable social safety nets.

Risk Management

Financial institutions use mortality tables in risk assessment models to evaluate and mitigate the risks associated with long-term investment products, structured finance, and other dependent financial services.

Statistical Models and Methods

Constructing a Life Table

Creating a life table involves several steps:

1. Data Collection: Gather data on death rates across various age groups.
2. Mortality Rates: Calculate the age-specific mortality rates.
3. Survivorship Function: Use the mortality rates to derive the survivorship function.
4. Life Expectancy: Compute the life expectancy using the survivorship function.

Parametric and Non-Parametric Models

Recent advancements in statistical methods have introduced both parametric and non-parametric models to fit mortality data. Parametric models might include Gompertz, Weibull, or Makeham models which assume specific functional forms of mortality rates.

Machine Learning and Artificial Intelligence

AI and machine learning algorithms are now being employed to analyze large volumes of life and health data to create more accurate mortality tables. These algorithms can account for non-linear dependencies and interaction effects among various factors contributing to mortality.

Mortality Table Providers

Many organizations and institutions produce and maintain mortality tables:

• Society of Actuaries (SOA) (https://www.soa.org/): Provides updated tables used by actuaries in North America.
• Human Mortality Database (HMD) (https://www.mortality.org/): Offers a comprehensive set of mortality data for researchers globally.
• U.S. Social Security Administration (SSA) (https://www.ssa.gov/): Provides public life tables used for social security planning.

Future Trends and Developments

With the advancement in healthcare, biotechnology, and data science, mortality tables are continually being refined and improved. Personalized mortality tables, driven by genetic data and individual health metrics, are emerging as the next frontier. Moreover, the integration of IoT (Internet of Things) devices for health monitoring and AI for predictive analytics will revolutionize how mortality data is collected and analyzed.

Conclusion

Mortality tables are indispensable tools in finance, insurance, and healthcare industries, offering critical insights into life expectancy, risk assessment, and financial planning. The ongoing evolution in data analytics and machine learning presents new opportunities for creating highly accurate and personalized mortality predictions, thereby improving risk management and resource allocation across various sectors.