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Optimal stopping with random maturity under nonlinear expectations

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  • Bayraktar, Erhan
  • Yao, Song

Abstract

We analyze an optimal stopping problem supγ∈TE¯0[Yγ∧τ0] with random maturity τ0 under a nonlinear expectation E¯0[⋅]:=supP∈PEP[⋅], where P is a weakly compact set of mutually singular probabilities. The maturity τ0 is specified as the hitting time to level 0 of some continuous index process X at which the payoff process Y is even allowed to have a positive jump. When P collects a variety of semimartingale measures, the optimal stopping problem can be viewed as a discretionary stopping problem for a player who can influence both drift and volatility of the dynamic of underlying stochastic flow.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:8:p:2586-2629
    DOI: 10.1016/j.spa.2016.12.001
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    References listed on IDEAS

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    1. 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.
    2. Kyoung Jin Choi & Hyeng Keun Koo, 2005. "A preference change and discretionary stopping in a consumption and porfolio selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 419-435, July.
    3. Bayraktar, Erhan & Yao, Song, 2012. "Quadratic reflected BSDEs with unbounded obstacles," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1155-1203.
    4. Erhan Bayraktar & Ioannis Karatzas & Song Yao, 2009. "Optimal Stopping for Dynamic Convex Risk Measures," Papers 0909.4948, arXiv.org, revised Nov 2009.
    5. Monique Jeanblanc & Peter Lakner & Ashay Kadam, 2004. "Optimal Bankruptcy Time and Consumption/Investment Policies on an Infinite Horizon with a Continuous Debt Repayment Until Bankruptcy," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 649-671, August.
    6. Frank Riedel, 2009. "Optimal Stopping With Multiple Priors," Econometrica, Econometric Society, vol. 77(3), pages 857-908, May.
    7. A. Cadenillas & S. P. Sethi, 1997. "Consumption-Investment Problem with Subsistence Consumption, Bankruptcy, and Random Market Coefficients," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 243-272, May.
    8. Erhan Bayraktar & Yu-Jui Huang, 2010. "On the Multi-Dimensional Controller and Stopper Games," Papers 1009.0932, arXiv.org, revised Jan 2013.
    9. Marcel Nutz & Jianfeng Zhang, 2012. "Optimal stopping under adverse nonlinear expectation and related games," Papers 1212.2140, arXiv.org, revised Sep 2015.
    10. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
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    Cited by:

    1. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    2. Denis Belomestny & Tobias Hübner & Volker Krätschmer, 2022. "Solving optimal stopping problems under model uncertainty via empirical dual optimisation," Finance and Stochastics, Springer, vol. 26(3), pages 461-503, July.
    3. Yu‐Jui Huang & Xiang Yu, 2021. "Optimal stopping under model ambiguity: A time‐consistent equilibrium approach," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 979-1012, July.

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