Wealth $10k, risk 50% on $9999 loss, recommends insure for $9900 premium.
The math is correct if you’re trying to optimize log(Wealth). log(10000)=4 and log(1)=0 so the mean is log(100)=2. This model assumes going bankrupt is infinitely bad, which is not accurate of an assumption, but it is not a bug.
Hmm, I guess I see why other calculators have at least some additional heuristics and aren’t straight Kelly. Going bankrupt is not infinitely bad in the US. If the insured has low wealth, there’s likely a loan attached to any large asset that really complicates the math. Making W just be “household wealth” also doesn’t model “I can replace the loss next paycheck”. I’m not sure what exactly the correct notion of wealth is here, but if wealth is small compared to future earnings, and replacing the loss can be deferred, these assumptions are incorrect.
And obviously, paying $10k premium to insure a 50% chance of a $10k loss is always a mistake for all wealth levels. You’re choosing to be bankrupt in 100% of possible worlds instead of 50%.
The math is correct if you’re trying to optimize log(Wealth). log(10000)=4 and log(1)=0 so the mean is log(100)=2. This model assumes going bankrupt is infinitely bad, which is not accurate of an assumption, but it is not a bug.
Hmm, I guess I see why other calculators have at least some additional heuristics and aren’t straight Kelly. Going bankrupt is not infinitely bad in the US. If the insured has low wealth, there’s likely a loan attached to any large asset that really complicates the math. Making W just be “household wealth” also doesn’t model “I can replace the loss next paycheck”. I’m not sure what exactly the correct notion of wealth is here, but if wealth is small compared to future earnings, and replacing the loss can be deferred, these assumptions are incorrect.
And obviously, paying $10k premium to insure a 50% chance of a $10k loss is always a mistake for all wealth levels. You’re choosing to be bankrupt in 100% of possible worlds instead of 50%.