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

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

Abstract

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

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    Cited by:

    1. Xindan Li & Dan Tang & Yongjin Wang & Xuewei Yang, 2014. "Optimal processing rate and buffer size of a jump-diffusion processing system," Annals of Operations Research, Springer, vol. 217(1), pages 319-335, June.
    2. 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.
    3. Noba, Kei, 2021. "On the optimality of double barrier strategies for Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 131(C), pages 73-102.
    4. Ning Cai & Xuewei Yang, 2021. "A Computational Approach to First Passage Problems of Reflected Hyperexponential Jump Diffusion Processes," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 216-229, January.
    5. Jiaen Xu & Chunwei Wang & Naidan Deng & Shujing Wang, 2023. "Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment," Mathematics, MDPI, vol. 11(7), pages 1-22, March.

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    More about this item

    Keywords

    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;
    All these keywords.

    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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