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On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency

Author

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  • Avanzi, Benjamin
  • Cheung, Eric C.K.
  • Wong, Bernard
  • Woo, Jae-Kyung

Abstract

We consider the dual model, which is appropriate for modeling the surplus of companies with deterministic expenses and stochastic gains, such as pharmaceutical, petroleum or commission-based companies. Dividend strategies for this model that can be found in the literature include the barrier strategy (e.g., Avanzi et al., 2007) and the threshold strategy (e.g., Cheung, 2008), where dividend decisions are made continuously. While in practice the financial position of a company is typically monitored frequently, dividend decisions are only made periodically along with the publication of its books. In this paper, we introduce a dividend barrier strategy whereby dividend decisions are made only periodically, but still allow ruin to occur at any time (as soon as the surplus is exhausted). This is in contrast to Albrecher et al. (2011a), who introduced periodic dividend payments in the Cramér–Lundberg surplus model, albeit with periodic ruin opportunities as well.

Suggested Citation

  • Avanzi, Benjamin & Cheung, Eric C.K. & Wong, Bernard & Woo, Jae-Kyung, 2013. "On a periodic dividend barrier strategy in the dual model with continuous monitoring of solvency," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 98-113.
  • Handle: RePEc:eee:insuma:v:52:y:2013:i:1:p:98-113
    DOI: 10.1016/j.insmatheco.2012.10.008
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    References listed on IDEAS

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    1. repec:spr:compst:v:67:y:2008:i:1:p:21-42 is not listed on IDEAS
    2. Gerber, Hans U. & Smith, Nathaniel, 2008. "Optimal dividends with incomplete information in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 227-233, October.
    3. Ng, Andrew C.Y., 2010. "On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 40(01), pages 281-306, May.
    4. Avanzi, Benjamin & Shen, Jonathan & Wong, Bernard, 2011. "Optimal Dividends and Capital Injections in the Dual Model with Diffusion," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(02), pages 611-644, November.
    5. Asmussen, Soren & Avram, Florin & Usabel, Miguel, 2002. "Erlangian Approximations for Finite-Horizon Ruin Probabilities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 32(02), pages 267-281, November.
    6. Albrecher, Hansjörg & Cheung, Eric C.K. & Thonhauser, Stefan, 2011. "Randomized Observation Periods for the Compound Poisson Risk Model: Dividends," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 41(02), pages 645-672, November.
    7. Avanzi, Benjamin & U. Gerber, Hans & S.W. Shiu, Elias, 2007. "Optimal dividends in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 111-123, July.
    8. Mazza, Christian & Rulliere, Didier, 2004. "A link between wave governed random motions and ruin processes," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 205-222, October.
    9. V. Ramaswami & Douglas Woolford & David Stanford, 2008. "The erlangization method for Markovian fluid flows," Annals of Operations Research, Springer, vol. 160(1), pages 215-225, April.
    10. Avanzi, Benjamin & Gerber, Hans U., 2008. "Optimal Dividends in the Dual Model with Diffusion," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 653-667, November.
    11. Albrecher, Hansjörg & Badescu, Andrei & Landriault, David, 2008. "On the dual risk model with tax payments," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1086-1094, June.
    12. Cheung, Eric C.K. & Drekic, Steve, 2008. "Dividend Moments in the Dual Risk Model: Exact and Approximate Approaches," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 399-422, November.
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    Citations

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    Cited by:

    1. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    2. Avanzi, Benjamin & Tu, Vincent & Wong, Bernard, 2014. "On optimal periodic dividend strategies in the dual model with diffusion," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 210-224.
    3. repec:eee:insuma:v:74:y:2017:i:c:p:135-146 is not listed on IDEAS
    4. repec:eee:apmaco:v:315:y:2017:i:c:p:1-12 is not listed on IDEAS
    5. Chen, Shumin & Wang, Xi & Deng, Yinglu & Zeng, Yan, 2016. "Optimal dividend-financing strategies in a dual risk model with time-inconsistent preferences," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 27-37.
    6. repec:eee:spapps:v:128:y:2018:i:1:p:255-290 is not listed on IDEAS
    7. Choi, Michael C.H. & Cheung, Eric C.K., 2014. "On the expected discounted dividends in the Cramér–Lundberg risk model with more frequent ruin monitoring than dividend decisions," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 121-132.

    More about this item

    Keywords

    Dual model; Barrier strategy; Erlangization; Dividends; Ruin;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G35 - Financial Economics - - Corporate Finance and Governance - - - Payout Policy

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