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Optimal buying at the global minimum in a regime switching model

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  • Yang, Aijun
  • Liu, Yue
  • Xiang, Ju
  • Yang, Hongqiang

Abstract

This paper addresses the problem of buying an asset at its expected globally minimal price, to that end, we model it as an optimal stopping problem with regime switching driven by a continuous-time Markov chain. We characterize the optimal stopping time by optimizing the value functions and writing them as solutions of a system of integral equations. Finally we develop a stochastic recursive algorithm for numerical implementation.

Suggested Citation

  • Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    • Handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:50-55
    DOI: 10.1016/j.mathsocsci.2016.08.005
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    References listed on IDEAS

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    1. William M. Boyce, 1970. "Stopping Rules for Selling Bonds," Bell Journal of Economics, The RAND Corporation, vol. 1(1), pages 27-53, Spring.
    2. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    3. Jin-Chuan Duan & Ivilina Popova & Peter Ritchken, 2002. "Option pricing under regime switching," Quantitative Finance, Taylor & Francis Journals, vol. 2(2), pages 116-132.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    6. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    7. G. Yin & Q. Zhang & K. Yin, 2003. "Constrained Stochastic Estimation Algorithms for a Class of Hybrid Stock Market Models," Journal of Optimization Theory and Applications, Springer, vol. 118(1), pages 157-182, July.
    8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    9. Jacques du Toit & Goran Peskir, 2009. "Selling a stock at the ultimate maximum," Papers 0908.1014, arXiv.org.
    10. Q. Zhang & G. Yin, 2004. "Nearly-Optimal Asset Allocation in Hybrid Stock Investment Models," Journal of Optimization Theory and Applications, Springer, vol. 121(2), pages 419-444, May.
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    Cited by:

    1. Yue Liu & Aijun Yang & Jijian Zhang & Jingjing Yao, 2020. "An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 827-843, March.

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