Asymptotic lower bounds for optimal tracking: A linear programming approach

Jiatu Cai; Mathieu Rosenbaum; Peter Tankov

doi:10.1214/16-AAP1264

Asymptotic lower bounds for optimal tracking: A linear programming approach

Jiatu Cai
, Mathieu Rosenbaum
, Peter Tankov

Laboratoire de Probabilités et Modèles Aléatoires
Ecole polytechnique

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

13 Citations (Scopus)

Résumé

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.

langue originale	Anglais
Pages (de - à)	2455-2514
Nombre de pages	60
journal	Annals of Applied Probability
Volume	27
Numéro de publication	4
Les DOIs	https://doi.org/10.1214/16-AAP1264
état	Publié - 1 août 2017
Modification externe	Oui

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abstract = "We consider the problem of tracking a target whose dynamics is modeled by a continuous It{\^o} 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.",

keywords = "Asymptotic lower bound, Impulse control, Linear programming, Occupation measure, Optimal tracking, Regular control, Singular control",

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KW - Asymptotic lower bound

KW - Impulse control

KW - Linear programming

KW - Occupation measure

KW - Optimal tracking

KW - Regular control

KW - Singular control

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Asymptotic lower bounds for optimal tracking: A linear programming approach

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