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Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach

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  • Jiatu Cai
  • Mathieu Rosenbaum
  • Peter Tankov

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.

Suggested Citation

  • Jiatu Cai & Mathieu Rosenbaum & Peter Tankov, 2015. "Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach," Papers 1510.04295, arXiv.org.
    • Handle: RePEc:arx:papers:1510.04295
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    References listed on IDEAS

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    Cited by:

    1. Huyên Pham, 2017. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Working Papers hal-01305929, HAL.
    2. Huy^en Pham, 2016. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Papers 1604.06609, arXiv.org, revised Mar 2017.
    3. Huyên Pham, 2016. "Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications ," Post-Print hal-01305929, HAL.
    4. Peter Bank & Mete Soner & Moritz Vo{ss}, 2015. "Hedging with Temporary Price Impact," Papers 1510.03223, arXiv.org, revised Jul 2016.
    5. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.

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