Glossary

A geometric mean is the type of average that fits compounding — the single constant growth rate that, applied period after period, ends up at the same final value as the actual sequence of period growth rates would produce.

The Kelly criterion is the position-sizing rule, derived by John Kelly in 1956, that maximizes the long-run growth rate of wealth by sizing each bet or investment as a specific fraction of current wealth determined by the bet's edge and its odds.

Log utility is the utility function in which each additional dollar of wealth contributes less than the prior dollar, following the logarithm — distinctive because maximizing expected log utility under multiplicative wealth dynamics coincides with maximizing the long-run growth rate of wealth.

Multiplicative dynamics describes the kind of process — common in investing and wealth growth — where each period's outcome is the previous period's value multiplied by a growth factor, so that gains and losses compound on top of each other rather than simply adding up.

Mutualization is the institutional arrangement, central to the ergodicity-economics treatment of cooperation, in which agents jointly own and bear the outcomes of a shared risk pool, so that each member's individual outcome becomes a function of the pool's aggregate experience.