ASYMPTOTIC LOWER BOUNDS FOR OPTIMAL TRACKING: A LINEAR PROGRAMMING APPROACH

• 成果类型: Article
• 署名作者: Cai, Jiatu; Rosenbaum, Mathieu; Tankov, Peter
• 署名单位: Universite Paris Cite; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1264
• 发表日期: 2017
• 页码: 2455-2514
• 关键词: controlled stochastic networks; singular ergodic control; transaction costs; IMPULSE CONTROL; DIFFUSIONS; EXISTENCE; jumps

摘要

We consider the problem of tracking a target whose dynamics is modeled by a continuous Ito 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.