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Lévy risk model with two-sided jumps and a barrier dividend strategy


  • Bo, Lijun
  • Song, Renming
  • Tang, Dan
  • Wang, Yongjin
  • Yang, Xuewei


In this paper, we consider a general Lévy risk model with two-sided jumps and a constant dividend barrier. We connect the ruin problem of the ex-dividend risk process with the first passage problem of the Lévy process reflected at its running maximum. We prove that if the positive jumps of the risk model form a compound Poisson process and the remaining part is a spectrally negative Lévy process with unbounded variation, the Laplace transform (as a function of the initial surplus) of the upward entrance time of the reflected (at the running infimum) Lévy process exhibits the smooth pasting property at the reflecting barrier. When the surplus process is described by a double exponential jump diffusion in the absence of dividend payment, we derive some explicit expressions for the Laplace transform of the ruin time, the distribution of the deficit at ruin, and the total expected discounted dividends. Numerical experiments concerning the optimal barrier strategy are performed and new empirical findings are presented.

Suggested Citation

  • Bo, Lijun & Song, Renming & Tang, Dan & Wang, Yongjin & Yang, Xuewei, 2012. "Lévy risk model with two-sided jumps and a barrier dividend strategy," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 280-291.
  • Handle: RePEc:eee:insuma:v:50:y:2012:i:2:p:280-291
    DOI: 10.1016/j.insmatheco.2011.12.002

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    References listed on IDEAS

    1. Pistorius, M. R., 2003. "On doubly reflected completely asymmetric Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 107(1), pages 131-143, September.
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    Cited by:

    1. Bo, Lijun & Yang, Xuewei, 2012. "Sequential maximum likelihood estimation for reflected generalized Ornstein–Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1374-1382.

    More about this item


    Risk model; Barrier strategy; Lévy process; Two-sided jump; Time of ruin; Deficit; Expected discounted dividend; Optimal dividend barrier; Integro-differential operator; Double exponential distribution; Reflected jump-diffusions; Laplace transform;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation


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