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Optimal Stopping for Dynamic Convex Risk Measures

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  • Erhan Bayraktar
  • Ioannis Karatzas
  • Song Yao

Abstract

We use martingale and stochastic analysis techniques to study a continuous-time optimal stopping problem, in which the decision maker uses a dynamic convex risk measure to evaluate future rewards. We also find a saddle point for an equivalent zero-sum game of control and stopping, between an agent (the "stopper") who chooses the termination time of the game, and an agent (the "controller", or "nature") who selects the probability measure.

Suggested Citation

  • Erhan Bayraktar & Ioannis Karatzas & Song Yao, 2009. "Optimal Stopping for Dynamic Convex Risk Measures," Papers 0909.4948, arXiv.org, revised Nov 2009.
  • Handle: RePEc:arx:papers:0909.4948
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    File URL: http://arxiv.org/pdf/0909.4948
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    Cited by:

    1. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    2. Daniel Fernholz & Ioannis Karatzas, 2012. "Optimal arbitrage under model uncertainty," Papers 1202.2999, arXiv.org.
    3. repec:eee:spapps:v:127:y:2017:i:8:p:2586-2629 is not listed on IDEAS
    4. 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.
    5. Kardaras, Constantinos & Robertson, Scott, 2012. "Robust maximization of asymptotic growth," LSE Research Online Documents on Economics 44994, London School of Economics and Political Science, LSE Library.
    6. Irina Penner & Anthony Reveillac, 2013. "Risk measures for processes and BSDEs," Working Papers hal-00814702, HAL.
    7. Erhan Bayraktar & Song Yao, 2013. "On the Robust Optimal Stopping Problem," Papers 1301.0091, arXiv.org, revised Apr 2016.
    8. Erhan Bayraktar & Zhou Zhou, 2012. "On controller-stopper problems with jumps and their applications to indifference pricing of American options," Papers 1212.4894, arXiv.org, revised Nov 2013.
    9. Irina Penner & Anthony Réveillac, 2015. "Risk measures for processes and BSDEs," Finance and Stochastics, Springer, vol. 19(1), pages 23-66, January.
    10. Irina Penner & Anthony Reveillac, 2013. "Risk measures for processes and BSDEs," Papers 1304.4853, arXiv.org.
    11. Bayraktar, Erhan & Yao, Song, 2017. "Optimal stopping with random maturity under nonlinear expectations," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2586-2629.

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