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On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy models

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  • Avanzi, Benjamin
  • Pérez, José-Luis
  • Wong, Bernard
  • Yamazaki, Kazutoshi

Abstract

The expected present value of dividends is one of the classical stability criteria in actuarial risk theory. In this context, numerous papers considered threshold (refractive) and barrier (reflective) dividend strategies. These were shown to be optimal in a number of different contexts for bounded and unbounded payout rates, respectively.

Suggested Citation

  • Avanzi, Benjamin & Pérez, José-Luis & Wong, Bernard & Yamazaki, Kazutoshi, 2017. "On optimal joint reflective and refractive dividend strategies in spectrally positive Lévy models," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 148-162.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:148-162
    DOI: 10.1016/j.insmatheco.2016.10.010
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    References listed on IDEAS

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    1. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "Refraction–Reflection Strategies In The Dual Model," ASTIN Bulletin, Cambridge University Press, vol. 47(1), pages 199-238, January.
    2. Avanzi, Benjamin & Shen, Jonathan & Wong, Bernard, 2011. "Optimal Dividends and Capital Injections in the Dual Model with Diffusion," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 611-644, November.
    3. Stéphane Loisel & Hans-U. Gerber, 2012. "Why ruin theory should be of interest for insurance practitioners and risk managers nowadays," Post-Print hal-00746231, HAL.
    4. 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.
    5. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2014. "Optimal dividends in the dual model under transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 133-143.
    6. 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.
    7. Erhan Bayraktar & Masahiko Egami, 2008. "Optimizing venture capital investments in a jump diffusion model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 67(1), pages 21-42, February.
    8. Yin, Chuancun & Wen, Yuzhen, 2013. "Optimal dividend problem with a terminal value for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 769-773.
    9. Chuancun Yin & Yuzhen Wen, 2013. "Optimal dividends problem with a terminal value for spectrally positive Levy processes," Papers 1302.6011, arXiv.org.
    10. Afonso, Lourdes B. & Cardoso, Rui M.R. & Egídio dos Reis, Alfredo D., 2013. "Dividend problems in the dual risk model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 906-918.
    11. Asmussen, Søren & Avram, Florin & Pistorius, Martijn R., 2004. "Russian and American put options under exponential phase-type Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 79-111, January.
    12. Benjamin Avanzi & Vincent Tu & Bernard Wong, 2016. "A Note on Realistic Dividends in Actuarial Surplus Models," Risks, MDPI, vol. 4(4), pages 1-9, October.
    13. Ng, Andrew C.Y., 2010. "On the Upcrossing and Downcrossing Probabilities of a Dual Risk Model With Phase-Type Gains," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 281-306, May.
    14. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 359-372, September.
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    Citations

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    Cited by:

    1. Wenyuan Wang & Yuebao Wang & Ping Chen & Xueyuan Wu, 2022. "Dividend and Capital Injection Optimization with Transaction Cost for Lévy Risk Processes," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 924-965, September.
    2. Czarna, Irmina & Pérez, José-Luis & Yamazaki, Kazutoshi, 2018. "Optimality of multi-refraction control strategies in the dual model," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 148-160.
    3. Boxma, Onno & Frostig, Esther, 2018. "The dual risk model with dividends taken at arrival," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 83-92.
    4. Albrecher, Hansjörg & Bäuerle, Nicole & Bladt, Martin, 2018. "Dividends: From refracting to ratcheting," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 47-58.
    5. Benjamin Avanzi & Debbie Kusch Falden & Mogens Steffensen, 2022. "Stable Dividends under Linear-Quadratic Optimization," Papers 2210.03494, arXiv.org.

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    More about this item

    Keywords

    Surplus models; Optimal dividends; Threshold strategy; Barrier strategy; Transaction costs;
    All these keywords.

    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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