In the last article, we considered the implications of correlated parameters on predicting performance in the stock market. Today I want to expand the same considerations to the insurance industry, and we will find much more controversy here!

For off, we have to decide just what insurance is and what its purpose is. You can’t do the computations if you don’t really know what you are computing. For instance, it doesn’t take a rocket scientist to realize that neither health insurance nor social security will ever be allowed to operate under free market rules. That is okay with me but others will likely disagree.

But what about less controversial issues such as automobile or home protection insurance?

What is the function of either type of insurance beyond making a living for the sales personnel and the issuing corporation? In part, the usual function is to reduce the risk to individuals of catastrophic loss by spreading the cost around the large base, where is will be less noticeable.

In normal applications, insurance does not function to lower overall costs incurred due to risks (I’m obviously simplifying here by ignoring educational programs and aggressive litigation that might be supported by insurance companies). The goal is to make the future more predictable by assuming a constant low expense for most purchasers to avoid a disastrous unexpected large one as will happen to a few people. This works for most customers. In other words, it’s a probability game again, and it full of all the paradoxes we have previously considered. In fact, these paradoxes can work to a salesperson’s advantage in attracting new customers.

The simple vision of providing insurance, which uniformly spreads risk, does not last long. As soon as we enter the market for coverage, we naturally want to get the cheapest, best policy we can. One way to lower costs to the majority of people is to identify persons who are at a greater than normal risk of making a claim and then eliminating them from the shared risk pool. Alternatively, everyone can be allowed to purchase a policy, but the price varies with the perceived or computed risk. Again, this sounds simple and fair; the insurer collects a lot of data and correlates it with any parameter that seems to eliminate some fraction of the randomness in suffering loss. People with a history of bumping into things with their automobiles and causing injuries and property damage can reasonably be expected to continue that pattern and therefore will get more back from their insurance fees than people who have driven for years and never had an incident (and are therefore net losers in a sense). One obvious question is “What is a pattern of loss versus a couple of unrelated unlucky events?”

We are accustomed to age-related automobile premiums. Teenagers pay more for the same coverage than a mature person would pay. Elderly persons can expect to see higher premiums. However, if the responsibility of the insurer is to provide coverage at the minimum risk to the company (i.e. by being profitable), then any parameter that can be measured and shown to correlate with risk must be used to compute reasonable premiums. This includes measuring parameters that are generally considered not socially acceptable like race, ethnicity, religion, gender, and sexual orientation. The mathematics is not socially conscious.
It makes sense to base life insurance premiums of the current age of the purchaser. A healthy twenty-year-old should pay less than an eighty-year-old person for the same coverage, but what happens as DNA testing becomes less expensive and the de-coding more well-known? Should we all submit to DNA testing to get health and life insurance? The results certainly change the estimates of likelihood of having a genetically-linked disease or dying early.

Should home insurance rate calculations be allowed to vary by the crime statistics in the neighborhood? Does your fire insurance vary with the distance of your house from a fire hydrant? Should non-smokers and/or non-alcohol users get a lower premium?

Remember, any time a parameter is excluded from the computation, the bulk of customers end up paying more for their insurance. Is that fair? What is insurance anyway?

Obviously the considerations in establishing insurance protocols are heavily weighted by societal considerations to the extent that I have a difficult time trying to define operationally just what is the purpose of insurance - not as it is advertised, but as it exists from a mathematical point of view.

The decision theory, statistics, and probability calculations are simple and straightforward. The social considerations are complex. Yet many citizens are brainwashed to think the societal considerations are simple and the mathematical ones complex. That is why we argue about politics and religion, but rarely argue about decision theory.

For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.