IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i3d10.1007_s11009-020-09795-w.html
   My bibliography  Save this article

Optimal Investment and Reinsurance Under the Gamma Process

Author

Listed:
  • Bohan Li

    (Nankai University)

  • Junyi Guo

    (Nankai University)

Abstract

In this paper, the insurance company invests its wealth in a capital market composed of a riskless asset and a risky asset. The aggregate claim process of the insurance company is modeled by the Gamma process so as to make it closer to the reality. In practice, the insurance company provides not only those policies with large lose coverings but also policies with small ones. The Gamma process can describe this characteristic better than the compound Poisson process. It is assumed that the insurance company can purchase proportional reinsurance or excess-of-loss reinsurance. Two kinds of optimization problems are considered: maximizing the expected utility of the terminal wealth and minimizing the probability of ruin. For the problem of maximizing the expected utility of the terminal wealth, the explicit optimal value functions and optimal strategies are obtained. For the problem of minimizing the ruin probability, a sufficient condition for the optimal value function and the optimal strategy is obtained.

Suggested Citation

  • Bohan Li & Junyi Guo, 2021. "Optimal Investment and Reinsurance Under the Gamma Process," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 893-923, September.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09795-w
    DOI: 10.1007/s11009-020-09795-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09795-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09795-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Liang, Xiaoqing & Young, Virginia R., 2018. "Minimizing the probability of ruin: Optimal per-loss reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 181-190.
    2. Wang, Wenyuan & Hu, Yijun, 2012. "Optimal loss-carry-forward taxation for the Lévy risk model," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 121-130.
    3. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    4. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 177-192, November.
    5. 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.
    6. S. David Promislow & Virginia Young, 2005. "Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(3), pages 110-128.
    7. Chuancun Yin & Yuzhen Wen, 2013. "Optimal dividends problem with a terminal value for spectrally positive Levy processes," Papers 1302.6011, arXiv.org.
    8. Pérez, José-Luis & Yamazaki, Kazutoshi, 2017. "On the optimality of periodic barrier strategies for a spectrally positive Lévy process," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 1-13.
    9. Bai, Lihua & Guo, Junyi, 2008. "Optimal proportional reinsurance and investment with multiple risky assets and no-shorting constraint," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 968-975, June.
    10. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    11. Meng, Hui & Zhang, Xin, 2010. "Optimal Risk Control for The Excess of Loss Reinsurance Policies," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 179-197, May.
    12. Yang, Hailiang & Zhang, Lihong, 2005. "Optimal investment for insurer with jump-diffusion risk process," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 615-634, December.
    13. Hipp, Christian & Taksar, Michael, 2010. "Optimal non-proportional reinsurance control," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 246-254, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gu, Ailing & Guo, Xianping & Li, Zhongfei & Zeng, Yan, 2012. "Optimal control of excess-of-loss reinsurance and investment for insurers under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 674-684.
    2. Shihao Zhu & Jingtao Shi, 2019. "Optimal Reinsurance and Investment Strategies under Mean-Variance Criteria: Partial and Full Information," Papers 1906.08410, arXiv.org, revised Jun 2020.
    3. Zhao, Hui & Rong, Ximin & Zhao, Yonggan, 2013. "Optimal excess-of-loss reinsurance and investment problem for an insurer with jump–diffusion risk process under the Heston model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 504-514.
    4. Yi, Bo & Li, Zhongfei & Viens, Frederi G. & Zeng, Yan, 2013. "Robust optimal control for an insurer with reinsurance and investment under Heston’s stochastic volatility model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 601-614.
    5. Guan, Guohui & Liang, Zongxia, 2014. "Optimal reinsurance and investment strategies for insurer under interest rate and inflation risks," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 105-115.
    6. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.
    7. Chen, Lv & Qian, Linyi & Shen, Yang & Wang, Wei, 2016. "Constrained investment–reinsurance optimization with regime switching under variance premium principle," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 253-267.
    8. Qicai Li & Mengdi Gu & Zhibing Liang, 2014. "Optimal excess-of-loss reinsurance and investment polices under the CEV model," Annals of Operations Research, Springer, vol. 223(1), pages 273-290, December.
    9. Xue, Xiaole & Wei, Pengyu & Weng, Chengguo, 2019. "Derivatives trading for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 40-53.
    10. Ya Huang & Xiangqun Yang & Jieming Zhou, 2017. "Robust optimal investment and reinsurance problem for a general insurance company under Heston model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 305-326, April.
    11. Liang, Zhibin & Yuen, Kam Chuen & Guo, Junyi, 2011. "Optimal proportional reinsurance and investment in a stock market with Ornstein-Uhlenbeck process," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 207-215, September.
    12. Liu, Bing & Meng, Hui & Zhou, Ming, 2021. "Optimal investment and reinsurance policies for an insurer with ambiguity aversion," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    13. Yang Shen & Bin Zou, 2021. "Mean-Variance Investment and Risk Control Strategies -- A Time-Consistent Approach via A Forward Auxiliary Process," Papers 2101.03954, arXiv.org.
    14. 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.
    15. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    16. Nian Yao & Zhiming Yang, 2017. "Optimal excess-of-loss reinsurance and investment problem for an insurer with default risk under a stochastic volatility model," Papers 1704.08234, arXiv.org.
    17. Meng, Hui & Liao, Pu & Siu, Tak Kuen, 2019. "Continuous-time optimal reinsurance strategy with nontrivial curved structures," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    18. Shen, Yang & Zou, Bin, 2021. "Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process," Insurance: Mathematics and Economics, Elsevier, vol. 97(C), pages 68-80.
    19. Li, Zhongfei & Zeng, Yan & Lai, Yongzeng, 2012. "Optimal time-consistent investment and reinsurance strategies for insurers under Heston’s SV model," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 191-203.
    20. Zeng, Yan & Li, Zhongfei, 2011. "Optimal time-consistent investment and reinsurance policies for mean-variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 145-154, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09795-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.