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Optimal dividends in the dual model under transaction costs

Author

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  • Bayraktar, Erhan
  • Kyprianou, Andreas E.
  • Yamazaki, Kazutoshi

Abstract

We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive Lévy process, an optimal strategy is given by a (c1,c2)-policy that brings the surplus process down to c1 whenever it reaches or exceeds c2 for some 0≤c1

Suggested Citation

  • 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.
  • Handle: RePEc:eee:insuma:v:54:y:2014:i:c:p:133-143
    DOI: 10.1016/j.insmatheco.2013.11.007
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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. Bayraktar, Erhan & Kyprianou, Andreas E. & Yamazaki, Kazutoshi, 2013. "On Optimal Dividends In The Dual Model," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 43(03), pages 359-372, September.
    3. 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.
    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. 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.
    6. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2011. "Optimal dividend and capital injection problem in the dual model with proportional and fixed transaction costs," European Journal of Operational Research, Elsevier, vol. 211(3), pages 568-576, June.
    7. 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.
    8. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    9. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
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    Citations

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    Cited by:

    1. repec:eee:spapps:v:128:y:2018:i:1:p:306-331 is not listed on IDEAS
    2. repec:eee:insuma:v:74:y:2017:i:c:p:135-146 is not listed on IDEAS
    3. Jos'e-Luis P'erez & Kazutoshi Yamazaki & Xiang Yu, 2017. "The bail-out optimal dividend problem under the absolutely continuous condition," Papers 1709.06348, arXiv.org.
    4. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2727-2751.
    5. repec:spr:joptap:v::y::i::d:10.1007_s10957-016-1050-7 is not listed on IDEAS
    6. Kazutoshi Yamazaki, 2017. "Phase-type Approximation of the Gerber-Shiu Function," Papers 1701.02798, arXiv.org.
    7. Ewa Marciniak & Zbigniew Palmowski, 2016. "On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums," Papers 1605.04584, arXiv.org.
    8. 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.
    9. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    10. 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.
    11. repec:eee:insuma:v:77:y:2017:i:c:p:1-13 is not listed on IDEAS
    12. repec:eee:insuma:v:79:y:2018:i:c:p:57-68 is not listed on IDEAS
    13. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    14. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407, arXiv.org.
    15. 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.
    16. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    17. repec:spr:joptap:v:167:y:2015:i:1:d:10.1007_s10957-014-0653-0 is not listed on IDEAS

    More about this item

    Keywords

    Dual model; Dividends; Impulse control; Spectrally positive Lévy processes; Scale functions;

    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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