IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v217y2025ics0167715224002566.html
   My bibliography  Save this article

Minimizing the penalized goal-reaching probability with multiple dependent risks

Author

Listed:
  • Huang, Ying
  • Peng, Jun

Abstract

We consider a robust optimal investment and reinsurance problem with multiple dependent risks for an Ambiguity-Averse Insurer (AAI), who wishes to minimize the probability that the value of the wealth process reaches a low barrier before a high goal. We assume that the insurer can purchase per-loss reinsurance for every class of insurance business and invest its surplus in a risk-free asset and a risky asset. Using the technique of stochastic control theory and solving the associated Hamilton-Jacobi-Bellman (HJB) equation, we derive the robust optimal investment-reinsurance strategy and the associated value function. We conclude that the robust optimal investment-reinsurance strategy coincides with the one without model ambiguity, but the value function differs. We also illustrate our results by numerical examples.

Suggested Citation

  • Huang, Ying & Peng, Jun, 2025. "Minimizing the penalized goal-reaching probability with multiple dependent risks," Statistics & Probability Letters, Elsevier, vol. 217(C).
    • Handle: RePEc:eee:stapro:v:217:y:2025:i:c:s0167715224002566
    DOI: 10.1016/j.spl.2024.110287
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002566
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110287?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Haluk Yener, 2015. "Maximizing survival, growth and goal reaching under borrowing constraints," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 2053-2065, December.
    2. Young, Virginia R. & Zhang, Yuchong, 2016. "Lifetime ruin under ambiguous hazard rate," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 125-134.
    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. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Optimal Investment to Minimize the Probability of Drawdown," Papers 1506.00166, arXiv.org, revised Feb 2016.
    5. Li, Danping & Young, Virginia R., 2019. "Optimal reinsurance to minimize the discounted probability of ruin under ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 143-152.
    6. Bai, Lihua & Cai, Jun & Zhou, Ming, 2013. "Optimal reinsurance policies for an insurer with a bivariate reserve risk process in a dynamic setting," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 664-670.
    7. Bayraktar, Erhan & Young, Virginia R., 2016. "Optimally investing to reach a bequest goal," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 1-10.
    8. 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.
    9. Angoshtari, Bahman & Bayraktar, Erhan & Young, Virginia R., 2016. "Minimizing the probability of lifetime drawdown under constant consumption," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 210-223.
    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. Virginia Young, 2004. "Optimal Investment Strategy to Minimize the Probability of Lifetime Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 8(4), pages 106-126.
    12. Xia Han & Zhibin Liang & Virginia R. Young, 2020. "Optimal reinsurance to minimize the probability of drawdown under the mean-variance premium principle," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(10), pages 879-903, November.
    13. Han, Xia & Liang, Zhibin & Zhang, Caibin, 2019. "Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown," Annals of Actuarial Science, Cambridge University Press, vol. 13(2), pages 268-294, September.
    14. Liang, Xiaoqing & Liang, Zhibin & Young, Virginia R., 2020. "Optimal reinsurance under the mean–variance premium principle to minimize the probability of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 128-146.
    15. Sid Browne, 1997. "Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 22(2), pages 468-493, May.
    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. Leonie Violetta Brinker, 2021. "Minimal Expected Time in Drawdown through Investment for an Insurance Diffusion Model," Risks, MDPI, vol. 9(1), pages 1-18, January.
    2. Landriault, David & Li, Bin & Li, Danping & Li, Dongchen, 2016. "A pair of optimal reinsurance–investment strategies in the two-sided exit framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 284-294.
    3. Yakun Liu & Jingchao Li & Jieming Zhou & Yingchun Deng, 2024. "Optimal Investment and Reinsurance to Maximize the Probability of Drawup Before Drawdown," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-34, September.
    4. Bayraktar, Erhan & Young, Virginia R., 2007. "Minimizing the probability of lifetime ruin under borrowing constraints," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 196-221, July.
    5. 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.
    6. 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.
    7. Young, Virginia R., 2017. "Purchasing casualty insurance to avoid lifetime ruin," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 133-142.
    8. 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.
    9. 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.
    10. Li, Zhongfei & Yao, Jing & Li, Duan, 2010. "Behavior patterns of investment strategies under Roy's safety-first principle," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(2), pages 167-179, May.
    11. Tong Qian & Cuixia Chen & Weijun Yin & Bing Liu, 2024. "Optimal Investment-reinsurance Strategies for an Insurer with Options Trading Under Model Ambiguity," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    12. Zheng, Xiaoxiao & Zhou, Jieming & Sun, Zhongyang, 2016. "Robust optimal portfolio and proportional reinsurance for an insurer under a CEV model," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 77-87.
    13. Junna Bi & Jun Cai & Yan Zeng, 2021. "Equilibrium reinsurance-investment strategies with partial information and common shock dependence," Annals of Operations Research, Springer, vol. 307(1), pages 1-24, December.
    14. Li, Yongwu & Li, Zhongfei, 2013. "Optimal time-consistent investment and reinsurance strategies for mean–variance insurers with state dependent risk aversion," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 86-97.
    15. Zhou, Jieming & Yang, Xiangqun & Guo, Junyi, 2017. "Portfolio selection and risk control for an insurer in the Lévy market under mean–variance criterion," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 139-149.
    16. Sheng Delei & Xing Linfang, 2018. "Optimal Insurance-Package and Investment Problem for an Insurer," Journal of Systems Science and Information, De Gruyter, vol. 6(1), pages 85-96, February.
    17. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    18. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    19. Bahman Angoshtari & Erhan Bayraktar & Virginia R. Young, 2015. "Optimal Investment to Minimize the Probability of Drawdown," Papers 1506.00166, arXiv.org, revised Feb 2016.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:stapro:v:217:y:2025:i:c:s0167715224002566. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.