The Kelly criterion is the optimal way to allocate one's bankroll over a lifetime to a series of bets assuming the actor's utility increases logarithmically with the amount of money won. Most importantly the criterion gives motivation to decide between investments with identical expected value but different risk of default. It essentially stipulates that the proportion of one's bankroll invested in a class of bets should be proportional to the expected value divided by the payoff in case it pans out.

Now, nothing in the formalism restricts the rule to bets or money for that matter, but is applicable to any situation an actor as assumed above faces uncertainty and possible payoff in utility. Aside from the obvious application to investments, e.g. bonds, this is also applicable to the purchase of insurance or cryonic services.

Buying an insurance can obviously be modeled as bet in the Kelly sense. A simple generalisation of the Kelly criterion leads to a formula that allows to incorporate losses.

An open question, to me at least, is if it possible to generalise the Kelly criterion to arbitrary probability distributions. Also, how can it be that integration over all payoffs for constant expected value evaluates as infinity?

Finally, how would a similar criterion look like for other forms of utility functions?

I did not put this question in the open thread because I think the Kelly criterion deserves more of a discussion and is immediately relevant to this site's interests.