On Growth-Optimality vs. Security Against Underperformance

The expected log utility of wealth (i.e., the growth-optimal or Kelly) criterion has been oft-studied in the management science literature. It leads to the highest asymptotic growth rate of wealth, and has no adjustable “preference parameters” that would otherwise need to be precisely “adjusted” to a specific individual's needs. But risk-control concerns led to alternative criteria that stress security against under performance over finite horizons. Large deviations theory enables a straightforward generalization of log utility's asymptotic analysis that incorporates these security concerns. The result is a power utility criterion that (like log utility) is free of an adjustable risk aversion parameter, because the latter is endogenously determined by expected utility maximization itself! A Bayesian formulation of the Occam's Razor Principle is used to illustrate the unavoidable reduction of scientific testability (i.e., the ability to more easily falsify) inherent in criterion functions that introduce additional adjustable parameters that are not directly observable.