In 1738 Daniel Bernoulli published his resolution of the St. Petersburg paradox: a game with infinite expected value that no rational person would pay an infinite amount to play. His solution was to replace expected monetary value with expected utility — a concave function of wealth that captures diminishing marginal returns.
By introducing the logarithmic utility function, Bernoulli formalised the intuition that losing £100 hurts more than gaining £100 helps. This asymmetry is the mathematical definition of risk aversion and the foundation of modern portfolio theory, insurance pricing, and optimal bet sizing.
The logarithmic utility function Bernoulli proposed turns out to maximise the long-run growth rate of wealth — a result later formalised by John Kelly. The Kelly criterion, widely used in quantitative trading for position sizing, is a direct descendant of Bernoulli's utility framework.
Position sizing, risk budgets, and portfolio construction all require a utility framework. We do not maximise expected return — we maximise risk-adjusted return, following the principle Bernoulli established three centuries ago.