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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]

We consider a Markovian queueing system with N heterogeneous service facilities, each of which has multiple servers available, linear holding costs, a fixed value of service and a first-come-first-serve queue discipline. Customers arriving in the system can be either rejected or sent to one of the N facilities. Two different types of control policies are considered, which we refer to as 'selfishly optimal' and 'socially optimal'. We prove the equivalence of two different Markov Decision Process formulations, and then show that classical M/M/1 queue results from the early literature on behavioural queueing theory can be generalized to multiple dimensions in an elegant way. In particular, the state space of the continuous-time Markov process induced by a socially optimal policy is contained within that of the selfishly optimal policy. We also show that this result holds when customers are divided into an arbitrary number of heterogeneous classes, provided that the service rates remain non-discriminatory. [ABSTRACT FROM AUTHOR]