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Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach

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  • Kiyoshi Suzuki

    (Portfolio Consulting Department, Nomura Securities Co., Ltd., Tokyo, 100-8130, Japan)

Abstract

Very few studies have explored the structure of optimal switching regimes. We extend the existing research on the infinite-horizon multiple-regime switching problem with an arbitrary number of switch options by replacing the linear running reward function with a quadratic function in the objective function. To make our analysis more rigorous, we establish the theoretical basis for the application of the simultaneous multiple-regime switches to the problem with the extended objective function, and provide the sufficient condition under which each certain separated region in the space includes, at most, one single connected optimal switching region, which determines the structure of the optimal switching regions, and we identify the structure of the optimal switching regions for the particular problem.

Suggested Citation

  • Kiyoshi Suzuki, 2021. "Infinite-Horizon Optimal Switching Regions for a Pair-Trading Strategy with Quadratic Risk Aversion Considering Simultaneous Multiple Switchings: A Viscosity Solution Approach," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 336-360, February.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:1:p:336-360
    DOI: 10.1287/moor.2020.1059
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    References listed on IDEAS

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    1. El Asri, Brahim, 2013. "Stochastic optimal multi-modes switching with a viscosity solution approach," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 579-602.
    2. Metcalf, Gilbert E. & Hassett, Kevin A., 1995. "Investment under alternative return assumptions Comparing random walks and mean reversion," Journal of Economic Dynamics and Control, Elsevier, vol. 19(8), pages 1471-1488, November.
    3. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    4. Kiyoshi Suzuki, 2018. "Optimal pair-trading strategy over long/short/square positions—empirical study," Quantitative Finance, Taylor & Francis Journals, vol. 18(1), pages 97-119, January.
    5. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
    6. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    7. Tsekrekos, Andrianos E., 2010. "The effect of mean reversion on entry and exit decisions under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 725-742, April.
    8. Said Hamadène & Monique Jeanblanc, 2007. "On the Starting and Stopping Problem: Application in Reversible Investments," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 182-192, February.
    9. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    10. Duy Nguyen & Jingzhi Tie & Qing Zhang, 2014. "An Optimal Trading Rule Under a Switchable Mean-Reversion Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 145-163, April.
    11. Sarkar, Sudipto, 2003. "The effect of mean reversion on investment under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 377-396, November.
    12. Erhan Bayraktar & Masahiko Egami, 2010. "On the One-Dimensional Optimal Switching Problem," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 140-159, February.
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