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Optimal Stopping and Maximal Inequalities for Linear Diffusions

Author

Listed:
  • S. E. Graversen

    (University of Aarhus, Ny Munkegade)

  • G. Peškir

    (University of Aarhus, Ny Munkegade)

Abstract

Given a linear diffusion the solution is found to the optimal stopping problem where the gain is given by the maximum of the process and the cost is proportional to the duration of time. The optimal stopping boundary is shown to be the maximal solution of a nonlinear differential equation expressed in terms of the scale function and the speed measure. Applications to maximal inequalities are indicated.

Suggested Citation

  • S. E. Graversen & G. Peškir, 1998. "Optimal Stopping and Maximal Inequalities for Linear Diffusions," Journal of Theoretical Probability, Springer, vol. 11(1), pages 259-277, January.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:1:d:10.1023_a:1021659328029
    DOI: 10.1023/A:1021659328029
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    Cited by:

    1. Gapeev, Pavel V. & Li, Libo, 2022. "Perpetual American standard and lookback options with event risk and asymmetric information," LSE Research Online Documents on Economics 114940, London School of Economics and Political Science, LSE Library.
    2. Gapeev, Pavel V., 2006. "On maximal inequalities for some jump processes," SFB 649 Discussion Papers 2006-060, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    3. Chen Jia, 2019. "Sharp Moderate Maximal Inequalities for Upward Skip-Free Markov Chains," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1382-1398, September.
    4. Pavel V. Gapeev & Peter M. Kort & Maria N. Lavrutich & Jacco J. J. Thijssen, 2022. "Optimal Double Stopping Problems for Maxima and Minima of Geometric Brownian Motions," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 789-813, June.
    5. Xian Chen & Yong Chen & Yumin Cheng & Chen Jia, 2024. "Moderate and $$L^p$$ L p Maximal Inequalities for Diffusion Processes and Conformal Martingales," Journal of Theoretical Probability, Springer, vol. 37(4), pages 2990-3014, November.
    6. János Engländer, 2020. "A Generalization of the Submartingale Property: Maximal Inequality and Applications to Various Stochastic Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 506-521, March.

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