Introduction: Why People Aren't Just Numbers

In the world of actuarial science, we often talk about "the population," but in reality, no two people are exactly alike. If you were pricing a life insurance policy, you wouldn't charge a 20-year-old Olympic athlete the same as an 80-year-old heavy smoker, right? This chapter explores heterogeneity (the differences between us), selection (how certain groups end up in our data), and how these factors influence the mortality and morbidity assumptions we use in our models.

Understanding these concepts is vital because if our assumptions are wrong, our prices will be wrong, and the company could lose money or fail to meet its obligations to stakeholders.

Heterogeneity: The Mix in the Pot

Heterogeneity is a fancy word for "diversity" or "difference." In an actuarial context, it means that a population is made up of many different subgroups, each with its own level of risk.

Why Heterogeneity Matters

If we treat a diverse group as if everyone is the "average," we run into problems. For example, if we use a single mortality rate for both smokers and non-smokers, the rate will be too high for non-smokers (who might go elsewhere for a cheaper deal) and too low for smokers (who will flock to us because we're underpricing their risk). This is why actuaries aim for homogeneity—grouping similar risks together.

Factors Contributing to Variation

Several factors cause mortality (death) and morbidity (illness) rates to vary across a population:

  • Region: Where someone lives can affect their health due to climate, local pollution levels, or the quality of the local healthcare system.
  • Social and Economic Environment: This includes factors like income, education, and occupation. Generally, higher socio-economic groups tend to have better health outcomes due to better diet, lower stress, and better access to medical care.
  • Lifestyle: Habits like smoking, alcohol consumption, and exercise levels.

Quick Tip: When setting assumptions, actuaries must decide how many "buckets" to create. Too many buckets make the data in each one too small to be reliable; too few buckets lead to unfair pricing.

Selection: Choosing the Group

Selection occurs when the lives included in a particular group are not representative of the general population. In CP1, we focus on several specific types of selection.

1. Temporary Initial Selection (TIS)

This happens when people first take out an insurance policy. Because they usually have to pass a medical check or answer health questions (underwriting), they are generally healthier than the average person of the same age. However, this "health advantage" wears off over time as new illnesses develop.

We represent the mortality rate for someone aged \(x\) who joined \(t\) years ago as \(q_{[x]+t}\). The square brackets \([x]\) indicate the age at which they were selected (joined).

2. Class Selection

This occurs when a group is defined by a specific characteristic that correlates with their risk. For example, people who buy "Preferred Lives" insurance policies are selecting themselves into a group that usually has lower mortality than the general public.

3. Mortality Convergence

Over time, the differences between the "selected" group and the general population start to disappear. This is called mortality convergence. Eventually, the fact that you passed a medical 30 years ago doesn't make you much healthier than anyone else your age today. Nature eventually catches up with everyone!

4. The Selective Effect of Decrements

A decrement is just a way someone leaves a data set (e.g., death, withdrawal, or surrendering a policy). Decrements can have a "selective effect" on the people who stay.
Example: If all the healthy people "withdraw" (cancel their policies) because they find a cheaper deal elsewhere, the people left in the insurance pool will be the ones who are too sick to get insurance elsewhere. This makes the remaining group's mortality much higher than expected.

Risk Classification: Solving the Problem

To deal with heterogeneity and selection, actuaries use risk classification. This is the process of grouping risks with similar characteristics to ensure fairness and financial stability.

Why do we need different mortality tables?

You cannot use the same mortality table for every product. For example:

  • Life Insurance: We need tables based on "assured lives" (people who have been underwritten). These people usually have lower mortality than the general public.
  • Pensioners: We need tables for people who have reached retirement. These people often have lower mortality (they live longer) because they have survived long enough to retire and often come from higher socio-economic backgrounds.

Key Takeaway: Using a "general population" table for a specific group of insured lives is a common mistake. You must match the table to the specific class of lives being modelled.

Common Pitfalls and How to Avoid Them

Don't worry if this feels like a lot to juggle. Here are a few things to keep in mind for your exam:

  • Confusing Heterogeneity with Selection: Remember, heterogeneity is about the existing differences in the world, while selection is about the process that brings a specific group of people into your data set.
  • Ignoring the "Healthy Participant" effect: Always consider if the people in your data set are likely to be healthier than average (e.g., because they are employed or can afford insurance).
  • Data Grouping: If your data groups are too small, your results will be "volatile" (they will jump around a lot). Aim for "optimal homogeneity"—the best balance between groups being similar and groups being large enough to trust.

Quick Review Box

Heterogeneity: Differences within a population (age, sex, region, smoker status).
Temporary Initial Selection: The temporary boost in health seen in newly insured people due to underwriting.
Class Selection: Differences in risk based on the category of the person (e.g., social class).
Decrements: Events like withdrawals that can change the health profile of the remaining group.
Convergence: The process where the mortality rates of different groups eventually meet as they age.

Note: For further reading on how these assumptions are used in the broader actuarial process, refer to the chapters on "Setting assumptions" and "Valuation of liabilities."