Even so, at some level of wealth you’ll leave more behind by saving up the premium and having your children inherit the compound interest instead. That point is found through the Kelly criterion.
(The Kelly criterion is indeed equal to concave utility, but the insurance company is so wealthy that individual life insurance payouts sit on the nearly linear early part of the utility curve, whereas for most individuals it does not.)
It is under no such assumption! If you have sufficient wealth you will leave something even if you die early, by virtue of already having the wealth.
If it’s easier, think of it as the child guarding the parent’s money and deciding whether to place a hedging bet on their parent’s death or not—using said parent’s money. Using the same Kelly formula we’ll find there is some parental wealth at which it pays more to let it compound instead of using it to pay for premia.
Even so, at some level of wealth you’ll leave more behind by saving up the premium and having your children inherit the compound interest instead. That point is found through the Kelly criterion.
(The Kelly criterion is indeed equal to concave utility, but the insurance company is so wealthy that individual life insurance payouts sit on the nearly linear early part of the utility curve, whereas for most individuals it does not.)
That is assuming you live sufficiently long. The point in life insurance is to make sure you leave something for your kids/spouse if you die soon.
It is under no such assumption! If you have sufficient wealth you will leave something even if you die early, by virtue of already having the wealth.
If it’s easier, think of it as the child guarding the parent’s money and deciding whether to place a hedging bet on their parent’s death or not—using said parent’s money. Using the same Kelly formula we’ll find there is some parental wealth at which it pays more to let it compound instead of using it to pay for premia.