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Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies

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  • Tse
  • Forsyth
  • Kennedy
  • Windcliff

Abstract

We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton--Jacobi--Bellman (HJB) partial differential equations (PDEs). In particular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic-variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the mean-variance strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian method results in significantly better accuracy than standard axis-aligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy.

Suggested Citation

  • Tse & Forsyth & Kennedy & Windcliff, 2013. "Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(5), pages 415-449, November.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:415-449
    DOI: 10.1080/1350486X.2012.755817
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    Citations

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    Cited by:

    1. Samuel Drapeau & Peng Luo & Alexander Schied & Dewen Xiong, 2019. "An FBSDE approach to market impact games with stochastic parameters," Papers 2001.00622, arXiv.org.
    2. Yang, Qing-Qing & Ching, Wai-Ki & Gu, Jia-Wen & Siu, Tak-Kuen, 2018. "Market-making strategy with asymmetric information and regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 408-433.
    3. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    4. Olivier Guéant, 2016. "The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making," Post-Print hal-01393136, HAL.
    5. Qing-Qing Yang & Wai-Ki Ching & Jia-Wen Gu & Tak Kwong Wong, 2017. "Optimal Liquidation Problems in a Randomly-Terminated Horizon," Papers 1709.05837, arXiv.org.
    6. Olivier Gu'eant & Jean-Michel Lasry & Jiang Pu, 2014. "A convex duality method for optimal liquidation with participation constraints," Papers 1407.4614, arXiv.org, revised Dec 2014.
    7. Taylor, Nick, 2016. "Roll strategy efficiency in commodity futures markets," Journal of Commodity Markets, Elsevier, vol. 1(1), pages 14-34.
    8. Ningyuan Chen & Steven Kou & Chun Wang, 2018. "A Partitioning Algorithm for Markov Decision Processes with Applications to Market Microstructure," Management Science, INFORMS, vol. 64(2), pages 784-803, February.

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