Earlier quoted context omitted.
I disagree. The optimal long term strategy for managing a portfolio of independent investments is to always pick a mix that maximizes the expected value of the log of your net worth. This leads to a more conservative investment strategy than the naive "maximize your expected value", and explains such things as why money-losing investments into buying insurance can be a really good idea. In general this is probably no…
Why log? I get that your utility function from money is non-linear, but I would expect a more accurate model to be a step-function, with large steps at "out of debt", "can tell a bad boss sayonara", "can buy a house", "can pay for kids' college eduaction", and "never have to work again". Equity payouts from a typical startup exit often line up nicely with the middle three, and if you hit the Google/Facebook jackpot,…
Independent investment opportunities generally have the effect of multiplying your value by a random amount over a specified interval. When you take logs, you are adding a random amount instead. From the strong law of large numbers, after enough intervals, it is statistically certain that the sum of the logs of those random numbers numbers will converge on the number of intervals times the expected value of the log of your investment strategy.
Therefore maximizing the expected value of the log maximizes the long term rate of return that you (with 100% probability) will observe.