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August 2017 Asymptotic lower bounds for optimal tracking: A linear programming approach
Jiatu Cai, Mathieu Rosenbaum, Peter Tankov
Ann. Appl. Probab. 27(4): 2455-2514 (August 2017). DOI: 10.1214/16-AAP1264

Abstract

We consider the problem of tracking a target whose dynamics is modeled by a continuous Itô 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. "Asymptotic lower bounds for optimal tracking: A linear programming approach." Ann. Appl. Probab. 27 (4) 2455 - 2514, August 2017. https://doi.org/10.1214/16-AAP1264

Information

Received: 1 December 2015; Revised: 1 September 2016; Published: August 2017
First available in Project Euclid: 30 August 2017

zbMATH: 1373.93376
MathSciNet: MR3693531
Digital Object Identifier: 10.1214/16-AAP1264

Subjects:
Primary: 93E20

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 2017
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