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The Dynkin game with regime switching and applications to pricing game options

Author

Listed:
  • Siyu Lv

    (Southeast University)

  • Zhen Wu

    (Shandong University)

  • Qing Zhang

    (University of Georgia)

Abstract

This paper is concerned with the Dynkin game (a zero-sum optimal stopping game). The dynamic of the system is modeled by a regime switching diffusion, in which the regime switching mechanism provides the structural changes of the random environment. The goal is to find a saddle point for the payoff functional up to one of the players exiting the game. Taking advantage of the method of penalization and the dynamic programming principle, the value function of the game problem is shown to be the unique viscosity solution to the associated variational inequalities. We also consider a financial example of pricing game option under a regime switching market. Both optimal stopping rules for the buyer and the seller and fair price of the option are numerically demonstrated in this example. All the results are markedly different from the traditional cases without regime switching.

Suggested Citation

  • Siyu Lv & Zhen Wu & Qing Zhang, 2022. "The Dynkin game with regime switching and applications to pricing game options," Annals of Operations Research, Springer, vol. 313(2), pages 1159-1182, June.
    • Handle: RePEc:spr:annopr:v:313:y:2022:i:2:d:10.1007_s10479-020-03656-y
    DOI: 10.1007/s10479-020-03656-y
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Yao, Song, 2015. "Doubly reflected BSDEs with integrable parameters and related Dynkin games," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4489-4542.
    2. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    3. Robert Elliott & Tak Siu, 2010. "On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy," Annals of Operations Research, Springer, vol. 176(1), pages 271-291, April.
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    Citations

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    Cited by:

    1. Marzougue, Mohamed, 2023. "Non-linear Dynkin games over split stopping times," Statistics & Probability Letters, Elsevier, vol. 193(C).

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