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Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization

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  • Ma, Jingtang
  • Li, Wenyuan
  • Zheng, Harry

Abstract

In this paper, we study the dual control approach for the optimal asset allocation problem in a continuous-time regime-switching market. We find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations. These bounds can be tightened with additional controls to the dual process. We suggest a Monte-Carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utility functions, including power, non-HARA and Yaari utilities. The latter two utilities are beyond the scope of any current methods available in finding the value function.

Suggested Citation

  • Ma, Jingtang & Li, Wenyuan & Zheng, Harry, 2017. "Dual control Monte-Carlo method for tight bounds of value function in regime switching utility maximization," European Journal of Operational Research, Elsevier, vol. 262(3), pages 851-862.
    • Handle: RePEc:eee:ejores:v:262:y:2017:i:3:p:851-862
    DOI: 10.1016/j.ejor.2017.04.056
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    References listed on IDEAS

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    5. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
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    7. Fu, Jun & Wei, Jiaqin & Yang, Hailiang, 2014. "Portfolio optimization in a regime-switching market with derivatives," European Journal of Operational Research, Elsevier, vol. 233(1), pages 184-192.
    8. Bian, Baojun & Zheng, Harry, 2015. "Turnpike property and convergence rate for an investment model with general utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 28-49.
    9. Robert J. Elliott & Vikram Krishnamurthy & Jörn Sass, 2008. "Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching models," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 244-270, July.
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    Cited by:

    1. Jingtang Ma & Wenyuan Li & Harry Zheng, 2017. "Dual control Monte Carlo method for tight bounds of value function under Heston stochastic volatility model," Papers 1710.10487, arXiv.org.
    2. Kamma, Thijs & Pelsser, Antoon, 2022. "Near-optimal asset allocation in financial markets with trading constraints," European Journal of Operational Research, Elsevier, vol. 297(2), pages 766-781.
    3. Thijs Kamma & Antoon Pelsser, 2019. "Near-Optimal Dynamic Asset Allocation in Financial Markets with Trading Constraints," Papers 1906.12317, arXiv.org, revised Oct 2019.

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