Partial‐Kelly Strategies and Expected Utility: Small‐Edge Asymptotics

Partial‐Kelly strategies, proposed because full‐Kelly strategies that use log of fortune as utility were found to be too risky, are examined from the perspective of maximizing expected utility. The results are as follows: (1) there is no utility function that is independent of the risks it confronts and that exactly has partial‐Kelly strategies as the optimal strategy; and (2) constant relative risk aversion utility, with the constant relative risk parameter equal to the reciprocal of the partial‐Kelly parameter, is a good approximation to such a utility function, particularly when the investor's edge is small.