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arXiv · 1510.04295

Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach

Jiatu Cai·Mathieu Rosenbaum·Peter Tankov
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Abstract

We consider the problem of tracking a target whose dynamics is modeled by a continuous Itō semi-martingale. 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. A comprehensive list of examples with explicit expressions for the lower bounds is provided.

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Jiatu Cai, Mathieu Rosenbaum, Peter Tankov. 2015-10-14. Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach. https://arxiv.org/abs/1510.04295

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