I don’t think your case for how insurance companies make money (Appendix B) makes sense. The insurance company does not have logarithmic discounting on wealth, it will not be using Kelly to allocate bets. From the perspective of the company, it is purely dependent on the direct profitability of the bet—premium minus expected payout and overheads.
Separately, the claim that there is no alternative to Kelly is very weak. I guess you mean there is no formalized, mathematical alternative? Otherwise, I propose a very simple one: buy insurance if the cost of insurance is lower than the disutility of worrying about the bad outcomes covered by insurance. This is the ‘vibes based’ strategy you discuss at the beginning, but it is clearly superior to the Kelly calculator. In the case where Kelly says not to buy insurance, either:
you worry about the bad outcomes and that worry is more damaging than cost of insurance would be; you have lost utility
you do not worry about the bad outcomes more than cost of insurance; you would not have bought the insurance under vibes strategy either
Therefore the Kelly criterion can only be superior when it advises you to buy insurance for something you are not worried about. However, you are not likely to run this calculations about things you aren’t worried about, so these opportunities are hard to find.
Nevertheless, I’m glad the tool exists, because it might help me calibrate how much I should be worried about outcomes I can quantify.
The insurance company does not have logarithmic discounting on wealth, it will not be using Kelly to allocate bets. From the perspective of the company, it is purely dependent on the direct profitability of the bet—premium minus expected payout and overheads.
Not true. Risk management is a huge part of many types of insurance, and that is about finding the appropriate exposure to a risk—and this exposure is found through the Kelly criterion.
This matters less in some types of insurance (e.g. life, which has stable long-term rates and rare catastrophic events) but significantly in other types (liability, natural disaster-linked.)
This is only about maximising profit for a given level of risk, it has nothing to do with specific shapes of utility functions.
I don’t think your case for how insurance companies make money (Appendix B) makes sense. The insurance company does not have logarithmic discounting on wealth, it will not be using Kelly to allocate bets. From the perspective of the company, it is purely dependent on the direct profitability of the bet—premium minus expected payout and overheads.
Separately, the claim that there is no alternative to Kelly is very weak. I guess you mean there is no formalized, mathematical alternative? Otherwise, I propose a very simple one: buy insurance if the cost of insurance is lower than the disutility of worrying about the bad outcomes covered by insurance. This is the ‘vibes based’ strategy you discuss at the beginning, but it is clearly superior to the Kelly calculator. In the case where Kelly says not to buy insurance, either:
you worry about the bad outcomes and that worry is more damaging than cost of insurance would be; you have lost utility
you do not worry about the bad outcomes more than cost of insurance; you would not have bought the insurance under vibes strategy either
Therefore the Kelly criterion can only be superior when it advises you to buy insurance for something you are not worried about. However, you are not likely to run this calculations about things you aren’t worried about, so these opportunities are hard to find.
Nevertheless, I’m glad the tool exists, because it might help me calibrate how much I should be worried about outcomes I can quantify.
Not true. Risk management is a huge part of many types of insurance, and that is about finding the appropriate exposure to a risk—and this exposure is found through the Kelly criterion.
This matters less in some types of insurance (e.g. life, which has stable long-term rates and rare catastrophic events) but significantly in other types (liability, natural disaster-linked.)
This is only about maximising profit for a given level of risk, it has nothing to do with specific shapes of utility functions.