Fair-game gambling induced by an incentive fee
= Fair-game gambling induced by an incentive fee
{title2=$\mathbb P(Y=h)=(w_0-\ell)/(h-\ell)$}
With zero interest and zero risk premium, a manager whose current wealth lies between common-tangent contacts $\ell,h$ can improve <expected utility maximization> through a fair lottery paying those two values. The probability of $h$ is $(w_0-\ell)/(h-\ell)$. In a <Brownian filtration>, replicating a bounded terminal lottery gives a nonnegative wealth <martingale> throughout.