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Mean–variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics

Author

Listed:
  • Arti Singh

    (IIT Delhi)

  • Dharmaraja Selvamuthu

    (IIT Delhi)

Abstract

The efficient modeling of execution price path of an asset to be traded is an important aspect of the optimal trading problem. In this paper an execution price path based on the second order autoregressive process is proposed. The proposed price path is a generalization of the existing first order autoregressive price path in literature. Using dynamic programming method the analytical closed form solution of unconstrained optimal trading problem under the second order autoregressive process is derived. However in order to incorporate non-negativity constraints in the problem formulation, the optimal static trading problems under second order autoregressive price process are formulated. For a risk neutral investor, the optimal static trading problem of minimizing expected execution cost subject to non-negativity constraints is formulated as a quadratic programming problem. Whereas, for a risk averse investor the variance of execution cost is considered as a measure for the timing risk, and the mean–variance problem is formulated. Moreover, the optimal static trading problem subject to stochastic dominance constraints with mean–variance static trading strategy as the reference strategy is studied. Using Static approximation method the algorithm to solve proposed optimal static trading problems is presented. With numerical illustrations conducted on simulated data and the real market data, the significance of second order autoregressive price path, and the optimal static trading problems is presented.

Suggested Citation

  • Arti Singh & Dharmaraja Selvamuthu, 2017. "Mean–variance optimal trading problem subject to stochastic dominance constraints with second order autoregressive price dynamics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(1), pages 29-69, August.
    • Handle: RePEc:spr:mathme:v:86:y:2017:i:1:d:10.1007_s00186-017-0582-4
    DOI: 10.1007/s00186-017-0582-4
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. Xiaoqiang Cai & Kok-Lay Teo & Xiaoqi Yang & Xun Yu Zhou, 2000. "Portfolio Optimization Under a Minimax Rule," Management Science, INFORMS, vol. 46(7), pages 957-972, July.
    3. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    4. Reshma Khemchandani & Avikant Bhardwaj & Suresh Chandra, 2016. "Single asset optimal trading strategies with stochastic dominance constraints," Annals of Operations Research, Springer, vol. 243(1), pages 211-228, August.
    5. Gur Huberman & Werner Stanzl, 2005. "Optimal Liquidity Trading," Review of Finance, Springer, vol. 9(2), pages 165-200, June.
    6. Jim Gatheral & Alexander Schied, 2011. "Optimal Trade Execution Under Geometric Brownian Motion In The Almgren And Chriss Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 353-368.
    7. Eric Beutner, 2007. "Mean–variance hedging under transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 539-557, June.
    8. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
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    Cited by:

    1. Vrinda Dhingra & Amita Sharma & Shiv K. Gupta, 2021. "Sectoral portfolio optimization by judicious selection of financial ratios via PCA," Papers 2106.11484, arXiv.org, revised Jan 2023.

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