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Optimal dividend and equity issuance problem with proportional and fixed transaction costs


  • Peng, Xiaofan
  • Chen, Mi
  • Guo, Junyi


This paper investigates the optimal dividend problem of an insurance company, which controls risk exposure by reinsurance and by issuing new equity to protect from bankruptcy. Transaction costs are incurred by these business activities: reinsurance is non-cheap, dividend is taxed and fixed costs are generated by equity issuance. The goal of the company is to maximize the expected cumulative discounted dividend minus the expected discounted costs of equity issuance. This problem is formulated as a mixed regular-singular-impulse stochastic control problem. By solving the corresponding HJB equation, we obtain the analytical solutions of the optimal return function and the optimal strategy.

Suggested Citation

  • Peng, Xiaofan & Chen, Mi & Guo, Junyi, 2012. "Optimal dividend and equity issuance problem with proportional and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 576-585.
  • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:576-585
    DOI: 10.1016/j.insmatheco.2012.08.004

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    References listed on IDEAS

    1. Harrison, J. Michael & Taylor, Allison J., 1978. "Optimal control of a Brownian storage system," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 179-194, January.
    2. Grandell, Jan, 1979. "Empirical bounds for ruin probabilities," Stochastic Processes and their Applications, Elsevier, vol. 8(3), pages 243-255, May.
    3. Lihua Bai & Junyi Guo & Huayue Zhang, 2010. "Optimal excess-of-loss reinsurance and dividend payments with both transaction costs and taxes," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1163-1172.
    4. Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
    5. T. Choulli & M. Taksar & X. Y. Zhou, 2001. "Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 573-596.
    6. Taksar, Michael I. & Zhou, Xun Yu, 1998. "Optimal risk and dividend control for a company with a debt liability," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 105-122, May.
    7. 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.
    8. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    9. He, Lin & Liang, Zongxia, 2009. "Optimal financing and dividend control of the insurance company with fixed and proportional transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 88-94, February.
    10. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
    11. 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.
    12. Bjarne Hø jgaard & Michael Taksar, 1999. "Controlling Risk Exposure and Dividends Payout Schemes:Insurance Company Example," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 153-182.
    13. repec:spr:compst:v:72:y:2010:i:1:p:129-143 is not listed on IDEAS
    14. Bjarne Højgaard & Søren Asmussen & Michael Taksar, 2000. "Optimal risk control and dividend distribution policies. Example of excess-of loss reinsurance for an insurance corporation," Finance and Stochastics, Springer, vol. 4(3), pages 299-324.
    15. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893,
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    Cited by:

    1. Yao, Dingjun & Yang, Hailiang & Wang, Rongming, 2014. "Optimal risk and dividend control problem with fixed costs and salvage value: Variance premium principle," Economic Modelling, Elsevier, vol. 37(C), pages 53-64.
    2. repec:eee:insuma:v:74:y:2017:i:c:p:135-146 is not listed on IDEAS
    3. Chen, Mi & Peng, Xiaofan & Guo, Junyi, 2013. "Optimal dividend problem with a nonlinear regular-singular stochastic control," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 448-456.
    4. Cheng, Gongpin & Zhao, Yongxia, 2016. "Optimal risk and dividend strategies with transaction costs and terminal value," Economic Modelling, Elsevier, vol. 54(C), pages 522-536.
    5. 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


    Transaction costs; Mixed regular-singular-impulse control; HJB equation; Optimal dividend; Equity issuance;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


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