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Asymptotic optimal tracking: lower bounds and feedback strategies Tankov, Peter


We consider the problem of tracking a target whose dynamics is modeled by a continuous Itô semimartingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. Furthermore, we provide a comprehensive list of examples for which the lower bound is sharp and is attained by an explicit feedback strategy. This talk is based on the following papers: * Jiatu Cai, Mathieu Rosenbaum and Peter Tankov. Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach, arxiv preprint arXiv:1510.04295 * Jiatu Cai, Mathieu Rosenbaum and Peter Tankov. Asymptotic Optimal Tracking: Feedback Strategies, arxiv preprint arXiv:1603.09472

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