No Deal

"One drawback to many money management schemes is that they are wedded to the assumption of a logarithmic utility function. Essentially, this model assumes that the increase in people's utility for additional wealth remains constant for equal percentage increases in wealth. The problem with this model is that it is unbounded, eventually it will tell you to bet the ranch.



There is a technical objection to unbounded utility functions, which is known as the St. Petersburg Paradox. I can give the thrust of it with a simplified example. Suppose you have a billion dollars. If your utility function is unbounded, there has to be an amount of money that would have such a large utility that you would be willing to flip a coin for it against your entire billion-dollar net worth. There is no amount of money for which a sane person would gamble away a billion-dollar net worth on the flip of a coin..."