Your reply provides part of the missing piece. Given that I am over some kind of absolute measure of poverty, empirically having twice as much disposable income won't translate into twice as much insurable assets. This limits the portion of bankroll that can be spent for insurance. Also, Kelly assumed unlitimited offer of bets which is not that far from the truth. Theoretically I can ask the insurer to give twice the payout for twice the cost of insurance.
And still, your answer doesn't quite answer my original question. I asked for given (monthly) income, savings rate and maybe wealth, what is a optimal allocation of insurance and investments, e.g. bonds or equity? And even if assuming that I keep my current assets but double my income and wealth, Kelly still says to buy insurance, though you admit that anything Gates would want to insure against would ruin the insurer, but my intuition still says that Gates does not insure anything that I would, like a car, house or health costs.
Perhaps the problem lies in the dichotomy "buy insurance" versus "do not buy". It seems to me that you have, in fact, got three, not two, options:
a) Buy insurance from someone else
b) Spend the money
c) Save the money, in effect buying insurance from yourself.
I think option c) is showing up in your analysis as "do not buy insurance", which should be reserved for b). You are no doubt correct that Gates does not buy car insurance (unless perhaps he is forced to by law), but that does not mean he is not insured. In effect he is ac...
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