I know nothing about insurance, but treating this like one of those crappy interview questions, I'd say you multiply the probability of an incident with the cost of that incident times 1 million people, and that's your expected cost per year. Then you look at how much you charge each person and see if they're willing to pay.

Probably as someone else mentioned, dental insurance is expensive because even though routine dental work is cheaper than getting cancer / breaking a bone, it happens 100% of the time.

I generally assume the HN audience to be composed of entrepreneurs or would-be entrepreneurs. Understanding finance and forecasting is a very important skill. The math is very, very simple. It's a matter of breaking down a business into costs and income to calculate profits. Again, simple math. All businesses, from a local coffee shop to a multinational share a simple equation that can be summarized through "EBITDA" analysis:

https://goo.gl/A5nGML

You could start with expenses. I won't develop a comprehensive model here but here's a small list of what could cost an insurance company money.

  - Average number of claims per client per year
  - Average cost of claims
  - Regulatory compliance costs
  - Administration costs
  - Structural costs (buildings, desks, computers, cars, phones, etc.)
  - Cost of sales
  - Personnel costs (salaries, health insurance, benefits, taxes, HR, etc.)

Spending some time on Google would reveal lots more detail on how to create a model on the expense side. If you can find a publicly traded insurance company their SEC filings would contain lots of useful information on cost drivers in that industry. I would definitely look for these filings if available.

Next do income.

Simple version: How many clients? How much do they pay on average?

Complex: You need to divide clients into layers with different risk profiles. Each risk profile is likely to have to pay different premiums, etc. This connects with the cost side of the equation. I listed average cost of claims above, this isn't likely to be a realistic cost model. It might be OK for a quick first stab but you really need to model cost of claims in tiers with some relationship to statistical risk, etc. This requires some thought. Google, again, could be your friend here.

In some ways, to talk in programming terms, you almost want to create a class to represent an individual client (with all the relevant variables) and then instantiate a million of them by using realistic distribution criteria to decide how these variables, well, vary. For example: Out of a million people, in any given year: What's the likelihood of a non-fatal heart attack? What's the likelihood of broken bones? What's the likelihood of hospitalization? You then have to attach costs to these events.

You would then have to add a matrix of plans with different coverage structures, deductibles, etc. These plans will interact with the above to generate actual costs. Some people will have very low premiums but huge deductibles and light coverage. Others will opt for very higher premiums for more coverage and still have a deductibles structure. Google can provide ideas on what's out there.

This can get very, very complicated. The simple version can give someone a basic understanding of what's at play. Bottom line, there's a reason for which comprehensive dental insurance isn't commonplace and this kind of analysis reveals it.

To those of us used to the financial analysis of businesses the answer to this question is clear. I think it is important for people to try and understand how money works. A lot of the issues out there boil down to the masses not having this understanding. Every day politicians promise things that are firmly rooted in fantasy, a fantasy that is easily revealed with a quick dive into a spreadsheet. This is a huge problem.