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Recursive Optimal Stopping with Poisson Stopping Constraints

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Listed:
  • Gechun Liang
  • Wei Wei
  • Zhen Wu
  • Zhenda Xu

Abstract

This paper solves a recursive optimal stopping problem with Poisson stopping constraints using the penalized backward stochastic differential equation (PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random intervention times, and jumps play a significant role not only through the stopping times but also in the recursive objective functional and model coefficients. To solve the problem, we propose a decomposition method based on Jacod-Pham that allows us to separate the problem into a series of sub-problems between each pair of consecutive Poisson stopping times. To represent the value function of the recursive optimal stopping problem when the initial time falls between two consecutive Poisson stopping times and the generator is concave/convex, we leverage the comparison theorem of BSDEs with jumps. We then apply the representation result to American option pricing in a nonlinear market with Poisson stopping constraints.

Suggested Citation

  • Gechun Liang & Wei Wei & Zhen Wu & Zhenda Xu, 2024. "Recursive Optimal Stopping with Poisson Stopping Constraints," Papers 2407.17975, arXiv.org.
    • Handle: RePEc:arx:papers:2407.17975
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/5717 is not listed on IDEAS
    2. Idris Kharroubi & Thomas Lim, 2014. "Progressive Enlargement of Filtrations and Backward Stochastic Differential Equations with Jumps," Journal of Theoretical Probability, Springer, vol. 27(3), pages 683-724, September.
    3. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    4. Bayraktar, Erhan & Yao, Song, 2011. "Optimal stopping for non-linear expectations--Part I," Stochastic Processes and their Applications, Elsevier, vol. 121(2), pages 185-211, February.
    5. Lepeltier, J.-P. & Xu, M., 2005. "Penalization method for reflected backward stochastic differential equations with one r.c.l.l. barrier," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 58-66, November.
    6. Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org, revised Jul 2019.
    7. Gechun Liang & Eva Lutkebohmert & Wei Wei, 2012. "Funding Liquidity, Debt Tenor Structure, and Creditor's Belief: An Exogenous Dynamic Debt Run Model," Papers 1209.3513, arXiv.org, revised Mar 2015.
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