Following [\textit{U. Çetin} et al., Finance Stoch. 8, No. 3, 311--341 (2004; Zbl 1064.60083)] the authors consider a market in which limit orders are represented via a function \(S(t,x)\) modeling the unit price at time \(t\) for an order of size \(x\). They examine the profits realized by specialized traders over traditional traders by trading the asset at the marginal price \(S(t,0)\) rather than at \(S(t,x)\). Both these traders trade discretely in time. High frequency traders have the further advantage that they can break the size \(X_\tau\) of a given order at time \(\tau\) continuously over the period \((\tau,\tau+\varepsilon)\) and thus pay \(X_\tau S(\tau,0)+\int_\tau^{\tau+\varepsilon}Y_sdS(s,0)\) with \(\int_\tau^{\tau+\varepsilon}dY_s=X_\tau\). The analysis is carried out under the crucial assumption that the marginal price process \(S(t,0)\) admits an equivalent (local) martingale measure, a completely straightforward condition although in models with perfectly liquid assets.