Offer your thoughts or opinion on the input financial query or topic using your financial background.

For very high-net worth individuals, does it make sense to not have insurance?
Yes, and the math that tells you when is called the Kelly Criterion. The Kelly Criterion is on its face about how much you should bet on a positive-sum game. Imagine you have a game where you flip a coin, and if heads you are given 3 times your bet, and if tails you lose your bet.  Naively you'd think "great, I should play, and bet every dollar I have!" -- after all, it has a 50% average return on investment.  You get back on average 1.5$ for every dollar you bet, so every dollar you don't bet is a 0.5$ loss. But if you do this and you play every day for 10 years, you'll almost always end up bankrupt.  Funny that. On the other hand, if you bet nothing, you are losing out on a great investment.  So under certain assumptions, you neither want to bet everything, nor do you want to bet nothing (assuming you can repeat the bet almost indefinitely). The question then becomes, what percentage of your bankroll should you bet? Kelly Criterion answers this question.  The typical Kelly Criterion case is where we are making a bet with positive returns, not an insurance against loss; but with a bit of mathematical trickery, we can use it to determine how much you should spend on insuring against loss. An "easy" way to undertand the Kelly Criterion is that you want to maximize the logarithm of your worth in a given period.  Such a maximization results in the largest long-term value in some sense. Let us give it a try in an insurance case. Suppose you have a 1 million dollar asset.  It has a 1% chance per year of being destroyed by some random event (flood, fire, taxes, pitchforks). You can buy insurance against this for 2% of its value per year.  It even covers pitchforks. On its face this looks like a bad deal.  Your expected loss is only 1%, but the cost to hide the loss is 2%? If this is your only asset, then the loss makes your net worth 0.  The log of zero is negative infinity.  Under Kelly, any insurance (no matter how inefficient) is worth it.  This is a bit of an extreme case, and we'll cover why it doesn't apply even when it seems like it does elsewhere. Now suppose you have 1 million dollars in other assets.  In the insured case, we always end the year with 1.98 million dollars, regardless of if the disaster happens.  In the non-insured case, 99% of the time we have 2 million dollars, and 1% of the time we have 1 million dollars. We want to maximize the expected log value of our worth.  We have log(2 million - 20,000) (the insured case) vs 1% * log(1 million) + 99% * log(2 million). Or 13.7953 vs 14.49.  The Kelly Criterion says insurance is worth it; note that you could "afford" to replace your home, but because it makes up so much of your net worth, Kelly says the "hit it too painful" and you should just pay for insurance. Now suppose you are worth 1 billion.  We have log(1 billion - 20k) on the insured side, and 1%*log(999 million) + 99% * log(1 billion) on the uninsured side. The logs of each side are 21.42 vs 20.72.  (Note that the base of the logarithm doesn't matter; so long as you use the same base on each side). According to Kelly, we have found a case where insurance isn't worth it. The Kelly Criterion roughly tells you "if I took this bet every (period of time), would I be on average richer after (many repeats of this bet) than if I didn't take this bet?"  When the answer is "no", it implies self-insurance is more efficient than using external insurance.  The answer is going to be sensitive to the profit margin of the insurance product you are buying, and the size of the asset relative to your total wealth. Now, the Kelly Criterion can easily be misapplied.  Being worth financially zero in current assets can easily ignore non-financial assets (like your ability to work, or friends, or whatever).  And it presumes repeat to infinity, and people tend not to live that long. But it is a good starting spot. Note that the option of bankruptcy can easily make insurance not "worth it" for people far poorer; this is one of the reasons why banks insist you have insurance on your proprety. You can use Kelly to calculate how much insurance you should purchase at a given profit margin for the insurance company given your net worth and the risk involved.  This can be used in Finance to work out how much you should hedge your bets in an investment as well; in effect, it quantifies how having money makes it easier to make money.