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

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

Abstract

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

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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. Yongxia Zhao & Rongming Wang & Dingjun Yao & Ping Chen, 2015. "Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 272-295, October.
    3. Zhao, Yongxia & Chen, Ping & Yang, Hailiang, 2017. "Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 135-146.
    4. Kristoffer Lindensjo & Filip Lindskog, 2019. "Optimal dividends and capital injection under dividend restrictions," Papers 1902.06294, arXiv.org.
    5. 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.
    6. Xu, Ran & Woo, Jae-Kyung, 2020. "Optimal dividend and capital injection strategy with a penalty payment at ruin: Restricted dividend payments," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 1-16.
    7. Kristoffer Lindensjö & Filip Lindskog, 2020. "Optimal dividends and capital injection under dividend restrictions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 461-487, December.
    8. 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.
    9. 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.

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    More about this item

    Keywords

    Transaction costs; Mixed regular-singular-impulse control; HJB equation; Optimal dividend; Equity issuance;
    All these keywords.

    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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