Asymptotic optimal tracking: feedback strategies

This is a companion paper to [Cai, Rosenbaum and Tankov, Asymptotic lower bounds for optimal tracking: a linear programming approach, Arxiv: 1510.04295]. We consider a class of strategies of feedback form for the problem of tracking and study their performance under the asymptotic framework of the above reference. The strategies depend only on the current state of the system and keep the deviation from the target inside a time-varying domain. Although the dynamics of the target is non-Markovian, it turns out that such strategies are asympototically optimal for a large list of examples.