Optimal prediction of resistance and support levels.

Assuming that the asset priceXfollows a geometric Brownian motion, we study the optimal prediction problem where the infimum is taken over stopping timesofXandis a hidden aspiration level (having a potential of creating a resistance or support level forX). Adopting the ‘aspiration-level hypothesis’ and assuming thatis independent fromX, we show that a wide class of admissible (non-oscillatory) laws oflead to unique optimal trading boundaries that can be viewed as the ‘conditional median curves’ for the resistance and support levels (with respect toXandT). We prove the existence of these boundaries and derive the (nonlinear) integral equations which characterize them uniquely. The results are illustrated through some specific examples of admissible laws and their conditional median curves. [ABSTRACT FROM PUBLISHER]