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Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection

  • Nie, Tianyang
  • Rutkowski, Marek
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    We examine the connections between a novel class of multi-person stopping games with redistribution of payoffs and multi-dimensional reflected BSDEs in discrete- and continuous-time frameworks. Our goal is to provide an essential extension of classic results for two-player stopping games (Dynkin games) to the multi-player framework. We show the link between certain multi-period m-player stopping games and a new kind of m-dimensional reflected BSDEs. The existence and uniqueness of a solution to continuous-time reflected BSDEs are established. Continuous-time redistribution games are constructed with the help of reflected BSDEs and a characterization of the value of such stopping games is provided.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304414914000684
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    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 124 (2014)
    Issue (Month): 8 ()
    Pages: 2672-2698

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    Handle: RePEc:eee:spapps:v:124:y:2014:i:8:p:2672-2698
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    1. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71.
    2. Hamadène, S. & Lepeltier, J. -P., 2000. "Reflected BSDEs and mixed game problem," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 177-188, February.
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    5. Eilon Solan & Nicolas Vieille, 2002. "Quitting games - An example," Working Papers hal-00242995, HAL.
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    7. Hamadène, S., 1998. "Backward-forward SDE's and stochastic differential games," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 1-15, September.
    8. repec:spr:compst:v:66:y:2007:i:3:p:531-544 is not listed on IDEAS
    9. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
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