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Excess-of-loss reinsurance for a company with debt liability and constraints on risk reduction

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  • T. Choulli
  • M. Taksar
  • X. Y. Zhou

Abstract

We consider a problem of risk control and dividend optimization for a financial corporation facing a constant liability payment. More specifically we investigate the case of excess-of-loss reinsurance for an insurance company. In this scheme the insurance company diverts a part of its premium stream to another company, the reinsurer, in exchange for an obligation to pick up that amount of each claim which exceeds a certain level a. The objective of the insurer is to maximize the expected present value of total future dividend pay-outs. We consider cases when there is restriction on the rate of dividend pay-outs and when there is no restriction. In both cases we describe explicitly the optimal return function as well as the optimal policy.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:6:p:573-596
    DOI: 10.1088/1469-7688/1/6/301
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    Cited by:

    1. Zhang, Nan & Jin, Zhuo & Li, Shuanming & Chen, Ping, 2016. "Optimal reinsurance under dynamic VaR constraint," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 232-243.
    2. Zhuo Jin & George Yin & Chao Zhu, 2011. "Numerical Solutions of Optimal Risk Control and Dividend Optimization Policies under A Generalized Singular Control Formulation," Papers 1111.2584, arXiv.org.
    3. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    4. Guan, Huiqi & Liang, Zongxia, 2014. "Viscosity solution and impulse control of the diffusion model with reinsurance and fixed transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 109-122.
    5. Li, Peng & Zhou, Ming & Yao, Dingjun, 2022. "Optimal time for the excess of loss reinsurance with fixed costs," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 466-475.
    6. Liang, Zhibin & Young, Virginia R., 2012. "Dividends and reinsurance under a penalty for ruin," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 437-445.
    7. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    8. Jiaqin Wei & Hailiang Yang & Rongming Wang, 2010. "Classical and Impulse Control for the Optimization of Dividend and Proportional Reinsurance Policies with Regime Switching," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 358-377, November.
    9. Jin, Zhuo & Yang, Hailiang & Yin, G., 2015. "Optimal debt ratio and dividend payment strategies with reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 351-363.
    10. 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.
    11. Jin, Zhuo & Yin, G. & Wu, Fuke, 2013. "Optimal reinsurance strategies in regime-switching jump diffusion models: Stochastic differential game formulation and numerical methods," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 733-746.
    12. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    13. 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.
    14. Katia Colaneri & Julia Eisenberg & Benedetta Salterini, 2022. "Some Optimisation Problems in Insurance with a Terminal Distribution Constraint," Papers 2206.04680, arXiv.org.
    15. Egami, Masahiko & Young, Virginia R., 2009. "Optimal reinsurance strategy under fixed cost and delay," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 1015-1034, March.
    16. Guo, Xin & Liu, Jun & Zhou, Xun Yu, 2004. "A constrained non-linear regular-singular stochastic control problem, with applications," Stochastic Processes and their Applications, Elsevier, vol. 109(2), pages 167-187, February.
    17. 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.
    18. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    19. Liu, Wei & Hu, Yijun, 2014. "Optimal financing and dividend control of the insurance company with excess-of-loss reinsurance policy," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 121-130.

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