[lobochrome]

I remember a course on game theory at business school where we proved all insurance to be non-optimal. There were two ways to deal with catastrophic risk if I recall correctly, depending on the gain function:

a) if catastrophic risk is infinite - no premium will be acceptable due to price.

b) if catastrophic risk is discrete - it is optimal not to insure since the expected loss is ruinous anyways.

Led me to be highly skeptical of all insurance ever since. Paying out of pocket previously felt scary - now it feels good since I know I am saving money with acceptable risk.

Of course - I am more than happy to have mandatory insurance for healthcare, liability, etc. since I am not living in the US.

Going back to my game theory text books now :)

[choeger]

There are certain risks you simply cannot pay out-of-pocket: Car accidents (my car is insured to 20M in damages p.p.), house destruction (you usually already have one mortgage), or inability to work in your profession (e.g., by becoming blind). The former cases are so expensive you cannot expect to save money or take a loan and pay off the damages. The latter case impacts your ability to earn money in the first place.

An insurance company makes money because they don't expect many of these cases to happen at once. But that's not a position you should take.

[blitzar]

Also a pretty big difference between the payout/claim for my phone - capped at the price of a new phone, vs health, chronic condition, pain etc - unlimited.

Or you do what I do and live with the cracked back screen on your phone, because it is under a case anyway.

[echelon]

> my car is insured to 20M in damages p.p.

How much does that policy cost?

Are you hedging against running into a gas pipeline, school bus full of children, or something along those lines?

I'm honestly really curious about this.

[choeger]

This is Germany. I think the 20M is a legal requirement or derived from a legal requirement (by adding something on top).

This car insurance costs me around 40€/month, but there's a steep curve based on how many years you've been free of damages. A new driver would pay around 6 times as much, AFAIK.

The reasoning behind the high damage rate is indeed the risk to it injure a child for life. In that case the insurance will cover lifelong costs.

[MandieD]

Legal requirement for personal automobile liability insurance in Germany is 7.5M EUR for personal injuries and 1.2M for property damage. I was startled when I moved over here from Maryland, where $500k liability limit was the highest available from Geico at the time.

We have an umbrella liability policy for 100M EUR - generally recommended in Germany. Our home insurance is less than 300 EUR/yr. Most expensive insurance we have is long-term disability. However, we do not insure older used cars for anything other than liability, and certainly never insure consumer electronics. If a month’s pay could replace it, or it’s not something that absolutely must be replaced right away, we wing it. Insurance is for risks that we could not cover from savings or that would cause long-term financial hardship, not disappointments.

[vurpo]

There are issues that game theory can't solve. Take for example the St. Petersburg paradox. From Wikipedia:

"A casino offers a game of chance for a single player in which a fair coin is tossed at each stage. The initial stake begins at 2 dollars and is doubled every time heads appears. The first time tails appears, the game ends and the player wins whatever is in the pot. Thus the player wins 2 dollars if tails appears on the first toss, 4 dollars if heads appears on the first toss and tails on the second, 8 dollars if heads appears on the first two tosses and tails on the third, and so on. Mathematically, the player wins 2^(k+1) dollars, where k is the number of consecutive head tosses. What would be a fair price to pay the casino for entering the game?"

The expectation value for how much you'll win from this game is infinite, so a naive game theory assessment might conclude that it's worth paying up to an infinite amount of money to play this game.

Of course, the issue is that nobody has an infinite amount of dollars in their pocket. That, incidentally, is also the issue with your naive assessment of insurance policies.

[MengerSponge]

Fun fact: Insurance companies lost more money in the 2008 financial crisis than they had ever made in the entirety of human history.

I'm not sure if this still holds if you account for inflation. They really screwed the pooch on that one, so it wouldn't surprise me if it did.

[Rainymood]

In theory, theory and practice are the same.

If you are interested in this and want to further your studies in this field try looking up this thing called "Prospect theory", it's like game theory+.