In actuarial science, this is generally linked to the “utility theory” of money.
The general gist (as applied here) is that the lower amounts of money have a higher utility value - per dollar - than higher amounts. For example, the difference between being penniless and having $100K is much greater than the difference between having $400K and $500K, even though it’s the same amount of money. And so on.
When you pay your insurance premiums, you’re paying “off the top”. Meaning, you’re keeping the vast majority of your assets, and reducing your assets from their prior level by the value of those premiums. But if you had an uninsured loss, you’re losing off the bottom too – some of the money will be your last dollar.
For example, if your entire assets are $500K, and you insure that entire amount for $5,000, the insurance premium is the difference between $500K and $495K, which has a relatively low per-dollar value. But if you lose the $500K, then 99% of that loss is valued at more per thousand than the $5,000 premium, up to and including your very last $5,000 which is highest value of all.
In this context it’s been suggested that gamblers may have a negative risk curve.
Yes. Self-insurance is a gamble. It’s a gamble on which you get good odds when your criterion is to
maximize E[net worth]
but if the payout is very severe when your self-insurance gamble loses it is a bad bet by the Kelly criterion:
maximize E[log(net worth)]
The way to resolve this problem is to “self-insure” which large organizations do with many things.
And cheaper for a homeowner to have a high deductible, which will lower your rates considerably. Then you are “self-insured” for the little stuff (under $5,000.00 damage), but still covered if something major happens.
Non-profit insurance companies have a hard time raising capital, and capital is a fundamental requirement for insurance companies. (More important than for other companies, since insurance companies are heavily regulated for - among other things - their capital requirements.)
Mutual insurance companies are pretty close. They can make profits but they return those profits to policy holders as dividends or policy discounts. Mutual insurance - Wikipedia
There was the interesting case of the Tacoma Narrows Bridge. Most engineers and architects are familiar with this bridge as “Galloping Gertie,” because in 1940 it famously self-destructed in only moderate winds (search YouTube for amazing and terrifying film footage of the bridge swaying violently before its collapse). Washington state had purchased several separate insurance policies for the bridge, the sum of which was intended to cover its total cost. The agent for one of these policies, assuming that this big new sturdy bridge couldn’t possibly fail within his lifetime, simply pocketed the premium he received from the state, never activating the policy. When this was discovered after the collapse, he went to jail for his gamble.
The psychological problem I personally have with insurance is, when I buy it, I’m betting that I’m going to need it and they’re betting that that I won’t. The kicker is that I sincerely hope they’re right!
I’m only on the periphery of the insurance business, and there have been so many great replies above, but I do have one comment about the insurance-gambling comparison: in a casino, in a given month, the house will take in more money than they pay in winnings, because the known, constant mathematical odds are in their favor (for example, an American roulette wheel has 38 numbers, but a single number bet pays out at 36). Granted, games like blackjack may have more even odds (I’m guessing).
In insurance, the company (the “house”) doesn’t always win, and frequently loses, on a daily, monthly, even annual basis. Many property and casualty insurance companies leave particular markets or segments because they lose money year after year in that segment. It’s not an uncommon situation at all, and in those situations the company certainly hasn’t “made money off you”; they just used that money to pay claims, plus had to add some of their own*.
OK, sure, the reinsurers may kick in some, but reinsurance isn’t free
Gambling = taking a sure small loss for a small chance at a large gain.
Insurance = taking a sure small loss to avoid the small chance of a large loss.
I like the way economist David Friedman puts it in his book Hidden Order.
He describes the fact (also mentioned by Pasta and Fotheringay-Phipps) that for most people, money has a diminishing marginal utility: your first dollar is worth a lot more to you than your millionth, because that first dollar will be used to buy food in order to stay alive, while the millionth dollar will barely affect your happiness at all. Hence, for most people, an even-money bet is a bad bet because the money they risk losing is worth more to them than the money they might gain.
But in explaining insurance, Friedman adds the concept of moving money around between possible futures: when you insure your house against fire, you are moving money from a future in which you can afford to lose it, to a future in which you need that money really badly because your house just burnt down! So you’re essentially buying high-value dollars with low-value ones.
Although it has less to do with insurance, he also mentions the fact that there may be situations in which it is rational to have an increasing marginal utility function. E.g. if you are currently starving and don’t have enough money to buy food, getting a small amount of extra money will be worth a lot to you, whereas losing the same amount just means you will starve to death a bit faster. In such circumstances, it would make sense to accept any even-money bet offered to you.
Or let’s say you urgently need an expensive medical operation (and don’t have medical insurance), let’s say you need it within a week and it costs $100,000 but you only manage to scrounge up $50,000. In such a case, it would be rational to go to a casino and bet the whole amount on Red at the roulette table – sure, it’s a bet with a negative expected value when counted in money, but if you win you get to live, and if you lose you will be just as dead next week as if you had not played at all.
It’s all about your level of risk aversion. If you can tolerate a lot of risk, and are willing to consider losing the value of your house/car/whatever, then maybe no insurance is the way to go.
If you don’t like the idea of couch surfing, then paying a bit every 6 months to make sure you can recover from a catastrophe is worth it. My folks had their house burn to the ground 10 years ago. All they had was what they were wearing. My comfort level with risk means I pay my insurance.
The forerunner to the insurance industry was one form of a thing called “friendly societies”. These were basically cooperatives where all the members agreed to mutual benefits to each other, and originally had social aspects as well as financial protection. Friendly society type cooperatives for various purposes exist to this day. To be adequately capitalized for really major scale disasters, the ones concerned with such things essentially had to evolve into the insurance industry.
Essentially, this is what insurance is. Don’t think of it as gambling, think of it as mutual support. You and a hundred thousand of your closest friends agree to pay each other’s costs if there’s a catastrophe to any of you.
Isn’t this what Lloyds of London is/was? Basically the “Names” were reinsurers taking on a specific risk - they personally guaranteed the payouts. As long as the loss was not catastrophic, they made money taking premiums. When there was a major run on payouts, suddenly some rich people found they had signed up for the chance to pay huge amounts in cash.
Remember a major issue with health insurance was that the ones who didn’t need it much - the healthy-as-a-horse 25 to35 yo singles - did not buy it. What’s to worst case scenario - get hit by a truck or get cancer, be unable to work, go on welfare, your bills are paid by Medicaid, your only “asset” is that $100,000 student loan outstanding. Essentially, nothing to lose.
Once you get a house, a nice car, a steady income, retirement savings, a good income - the risk is that you could lose a lot more.
The same applies, for example, with a business that self-insures its vehicles. If you are only worried about vehicle damage, no problem. Greater/third party liability could be unlimited. (Jerry Pournelle, who wrote for Byte Magazine, describes an accident near his house - a car hit a transmission line, dropped 6,000v lines onto the 220 household feed lines, and every lightbulb or household electronics or electrical appliance for blocks around exploded. Except the computers plugged into the UPS he was testing. That’s the one in ten million risk that insurance is taking on for you. )
Here is Ambrose Bierce’s commentary on insurance, from the Devil’s Dictionary. Insurance Agent: My dear sir, that is a fine house—pray let me insure it. House Owner: With pleasure. Please make the annual premium so low that by the time when, according to the tables of your actuary, it will probably be destroyed by fire I will have paid you considerably less than the face [value] of the policy. Insurance Agent: O dear no—we could not afford to do that. We must fix the premium so that you will have paid more. House Owner: How, then, can I afford that? Insurance Agent: Why, your house may burn down at any time. There was Smith’s house, for example which— House Owner: Spare me—there was Brown’s house, on the contrary, and Jones’s house, and Robinson’s house which— Insurance Agent: Spare me! House Owner: Let us understand each other. You want me to pay you money on the supposition that something will occur previously to the time set by yourself for its occurrence. In other words, you expect me to bet that my house will not last as long as you say that it will probably last. Insurance Agent: But if your house burns without insurance it will be a total loss. House Owner: Beg your pardon—by your own actuary’s tables I shall probably have saved, when it burns, all the premiums I would otherwise have paid to you—amounting to more than the face [value] of the policy they would have bought. But suppose it to burn, uninsured, before the time upon which your figures are based. If I could not afford that, how could you if it were insured? Insurance Agent: O, we should make ourselves whole from our luckier ventures with other clients. Virtually, they pay your loss. House Owner: And virtually, then, don’t I help to pay their losses? Are not their houses as likely as mine to burn before they have paid you as much as you must pay them? The case stands this way: You expect to take more money from your clients than you pay to them, do you not? Insurance Agent: Certainly; if we did not— House Owner: I would not trust you with my money. Very well, then. If it is certain, with reference to the whole body of your clients, that they lose money on you it is probable, with reference to any one of them, that he will. It is these individual probabilities that make up the aggregate certainty. Insurance Agent: I will not deny it—but look at the figures in this pamph— House Owner: Heaven forbid! Insurance Agent: You spoke of saving the premiums which you would otherwise pay to me. Will you not be more likely to squander them? We offer you an incentive to thrift. House Owner: The willingness of A to take care of B’s money is not peculiar to insurance, but as a charitable institution you command esteem. Deign to accept its expression from a Deserving Object.
