With that assumption the equation compares your utility with and without insurance. Simple!
If you had some other utility function, like utility = $, then you should make insurance decisions differently.
I think the Kelly betting stuff is a big distraction, and that ppl with utility=$ shouldn’t bet like that. I think the result that Kelly betting maximizes long term $ bakes in assumptions about utility functions and is easily misunderstood—someone with utility=$ probably goes bankrupt but might become insanely rich AI is happy not to Kelly bet. (I haven’t explained this point properly, but recall reading about this and it’s just wrong on it’s face that someone with utility=$ should follow your formula)
I’m still a bit confused about this point of the Kelly criterion. I thought that actually this is the way to maximize expected returns if you value money linearly, and the log term comes from compounding gains.
That the log utility assumption is actually a separate justification for the Kelly criterion that doesn’t take into account expected compounding returns
The purpose if insurance is not to help us pay for things that we literally do not have enough money to pay for. It does help in that situation, but the purpose of insurance is much broader than that. What insurance does is help us avoid large drawndowns on our accumulated wealth, in order for our wealth to gather compound interest faster.
Think about that. Even though insurance is an expected loss, it helps us earn more money in the long run. This comes back to the Kelly criterion, which teaches us that the compounding effects on wealth can make it worth paying a little up front to avoid a potential large loss later.
This is a synonym for “if money compounds and you want more of it at lower risk”. So in a sense, yes, but it seems confusing to phrase it in terms of utility as if the choice was arbitrary and not determined by other constraints.
This is a synonym for “if money compounds and you want more of it at lower risk”.
No it’s not. In the real world, money compounds and I want more of it at lower risk. Also, in the real world, “utility = log($)” is false: I do not have a utility function, and if I did it would not be purely a function of money.
I either think this is wrong or I don’t understand.
What do you mean by ‘maximising compounding money?’ Do you mean maximising expected wealth at some specific point in the future? Or median wealth? Are you assuming no time discounting? Or do you mean maximising the expected value of some sort of area under the curve of wealth over time?
Your formula is only valid if utility = log($).
With that assumption the equation compares your utility with and without insurance. Simple!
If you had some other utility function, like utility = $, then you should make insurance decisions differently.
I think the Kelly betting stuff is a big distraction, and that ppl with utility=$ shouldn’t bet like that. I think the result that Kelly betting maximizes long term $ bakes in assumptions about utility functions and is easily misunderstood—someone with utility=$ probably goes bankrupt but might become insanely rich AI is happy not to Kelly bet. (I haven’t explained this point properly, but recall reading about this and it’s just wrong on it’s face that someone with utility=$ should follow your formula)
Is this true?
I’m still a bit confused about this point of the Kelly criterion. I thought that actually this is the way to maximize expected returns if you value money linearly, and the log term comes from compounding gains.
That the log utility assumption is actually a separate justification for the Kelly criterion that doesn’t take into account expected compounding returns
I’ve written about this here. Bottom line is, if you actually value money linearly (you don’t) you should not bet according to the Kelly criterion.
From the original post:
Click the link for a more in-depth explanation
This is a synonym for “if money compounds and you want more of it at lower risk”. So in a sense, yes, but it seems confusing to phrase it in terms of utility as if the choice was arbitrary and not determined by other constraints.
No it’s not. In the real world, money compounds and I want more of it at lower risk. Also, in the real world, “utility = log($)” is false: I do not have a utility function, and if I did it would not be purely a function of money.
I agree—sorry about the sloppy wording.
What I tried to say wad that “if you act like someone who maximises compounding money you also act like someone with utility that is log-money.”
I still disagree with that.
I either think this is wrong or I don’t understand.
What do you mean by ‘maximising compounding money?’ Do you mean maximising expected wealth at some specific point in the future? Or median wealth? Are you assuming no time discounting? Or do you mean maximising the expected value of some sort of area under the curve of wealth over time?