Human mobility is highly predictable. Individuals tend to only visit a few locations with high frequency, and to move among them in a certain sequence reflecting their habits and daily routine. This predictability has to be taken into account in the design of location privacy preserving mechanisms (LPPMs) in order to effectively protect users when they expose their whereabouts to location-based services (LBSs) continuously. In this paper, we describe a method for creating LPPMs tailored to a user's mobility profile taking into her account privacy and quality of service requirements. By construction, our LPPMs take into account the sequential correlation across the user's exposed locations, providing the maximum possible trajectory privacy, i.e., privacy for the user's past, present location, and expected future locations. Moreover, our LPPMs are optimal against a strategic adversary, i.e., an attacker that implements the strongest inference attack knowing both the LPPM operation and the user's mobility profile. The optimality of the LPPMs in the context of trajectory privacy is a novel contribution, and it is achieved by formulating the LPPM design problem as a Bayesian Stackelberg game between the user and the adversary. An additional benefict of our formal approach is that the design parameters of the LPPM are chosen by the optimization algorithm.