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Stochastic Perron for stochastic target games

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  • Erhan Bayraktar
  • Jiaqi Li

Abstract

We extend the stochastic Perron method to analyze the framework of stochastic target games, in which one player tries to find a strategy such that the state process almost surely reaches a given target no matter which action is chosen by the other player. Within this framework, our method produces a viscosity sub-solution (super-solution) of a Hamilton-Jacobi-Bellman (HJB) equation. We then characterize the value function as a viscosity solution to the HJB equation using a comparison result and a byproduct to obtain the dynamic programming principle.

Suggested Citation

  • Erhan Bayraktar & Jiaqi Li, 2014. "Stochastic Perron for stochastic target games," Papers 1408.6799, arXiv.org, revised Apr 2016.
    • Handle: RePEc:arx:papers:1408.6799
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    File URL: http://arxiv.org/pdf/1408.6799
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    References listed on IDEAS

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    1. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932, arXiv.org, revised Jan 2013.
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    Cited by:

    1. Erhan Bayraktar & Jiaqi Li, 2016. "Stochastic Perron for Stochastic Target Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1026-1054, September.
    2. Eulaiwi, Baban & Al-Hadi, Ahmed & Taylor, Grantley & Dutta, Saurav & Duong, Lien & Richardson, Grant, 2021. "Tax haven Use, the pricing of audit and Non-audit Services, suspicious matters reporting obligations and whistle blower hotline Facilities: Evidence from Australian financial corporations," Journal of Contemporary Accounting and Economics, Elsevier, vol. 17(2).
    3. Bruno Bouchard & Marcel Nutz, 2016. "Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 109-124, February.
    4. Bruno Bouchard & Marcel Nutz, 2015. "Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions," Post-Print hal-00846830, HAL.
    5. Yue Yang & Xiang Yu, 2019. "Optimal Entry and Consumption under Habit Formation," Papers 1903.04257, arXiv.org, revised Jul 2021.
    6. Junbeom Lee & Xiang Yu & Chao Zhou, 2019. "Lifetime Ruin under High-watermark Fees and Drift Uncertainty," Papers 1909.01121, arXiv.org, revised Oct 2020.

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