IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p40-d1305815.html
   My bibliography  Save this article

Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity

Author

Listed:
  • Dan Zhu

    (School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China)

  • Cuixia Chen

    (School of Insurance and Public Finance, Hebei Finance University, Baoding 071051, China)

  • Bing Liu

    (School of Finance, Nanjing University of Finance and Economics, Nanjing 210023, China)

Abstract

This study considers the optimal debt ratio and dividend payment policies for an insurer concerned about model misspecification. We assume that the insurer can invest all of its asset to the financial market and the ambiguity may exist in the risky asset. Taking into account the ambiguous situation, the insurer aims to maximize the expected utility of a discounted dividend payment until it ruins. Under some assumption, we prove that there exists classical solutions of the optimal debt ratio, dividend payment policies, and value functions that show that the existence of ambiguity can affect the optimal debt ratio and dividend policies significantly.

Suggested Citation

  • Dan Zhu & Cuixia Chen & Bing Liu, 2023. "Optimal Debt Ratio and Dividend Payment Policies for Insurers with Ambiguity," Mathematics, MDPI, vol. 12(1), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:40-:d:1305815
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/40/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/40/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    3. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    4. Qingbin Meng & Junna Bi, 2020. "On the dividends of the risk model with Markovian barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(5), pages 1272-1280, March.
    5. Dan Zhu & Chuancun Yin, 2018. "Stochastic Optimal Control of Investment and Dividend Payment Model under Debt Control with Time-Inconsistency," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, July.
    6. Paulsen, Jostein & Gjessing, Hakon K., 1997. "Optimal choice of dividend barriers for a risk process with stochastic return on investments," Insurance: Mathematics and Economics, Elsevier, vol. 20(3), pages 215-223, October.
    7. Chuancun Yin & Yuzhen Wen, 2013. "Optimal dividends problem with a terminal value for spectrally positive Levy processes," Papers 1302.6011, arXiv.org.
    8. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2022. "A perturbation approach to optimal investment, liability ratio, and dividend strategies," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(2), pages 165-188, February.
    9. Jun Cai & Hans Gerber & Hailiang Yang, 2006. "Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 94-108.
    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. Feng, Yang & Zhu, Jinxia & Siu, Tak Kuen, 2021. "Optimal risk exposure and dividend payout policies under model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 1-29.
    2. 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.
    3. Benjamin Avanzi & Debbie Kusch Falden & Mogens Steffensen, 2022. "Stable Dividends under Linear-Quadratic Optimization," Papers 2210.03494, arXiv.org.
    4. Benjamin Avanzi & Jos'e-Luis P'erez & Bernard Wong & Kazutoshi Yamazaki, 2016. "On optimal joint reflective and refractive dividend strategies in spectrally positive L\'evy models," Papers 1607.01902, arXiv.org, revised Nov 2016.
    5. Zhang, Jiannan & Chen, Ping & Jin, Zhuo & Li, Shuanming, 2021. "On a class of non-zero-sum stochastic differential dividend games with regime switching," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    6. Yuen, Kam-Chuen & Zhou, Ming & Guo, Junyi, 2008. "On a risk model with debit interest and dividend payments," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2426-2432, October.
    7. Zhuo Jin & Zuo Quan Xu & Bin Zou, 2020. "A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies," Papers 2012.06703, arXiv.org, revised May 2021.
    8. Boxma, Onno & Frostig, Esther, 2018. "The dual risk model with dividends taken at arrival," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 83-92.
    9. Wei Wang, 2015. "The Perturbed Sparre Andersen Model with Interest and a Threshold Dividend Strategy," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 251-283, June.
    10. 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.
    11. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2022. "Stackelberg differential game for insurance under model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 128-145.
    12. Chuancun Yin & Kam Chuen Yuen, 2014. "Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs," Papers 1409.0407, arXiv.org.
    13. Rhys Bidder & Ian Dew-Becker, 2016. "Long-Run Risk Is the Worst-Case Scenario," American Economic Review, American Economic Association, vol. 106(9), pages 2494-2527, September.
    14. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    15. Hansjoerg Albrecher & Pablo Azcue & Nora Muler, 2020. "Optimal ratcheting of dividends in a Brownian risk model," Papers 2012.10632, arXiv.org.
    16. Luo, Yulei & Young, Eric R., 2016. "Induced uncertainty, market price of risk, and the dynamics of consumption and wealth," Journal of Economic Theory, Elsevier, vol. 163(C), pages 1-41.
    17. Corgnet, Brice & Hernán-González, Roberto & Kujal, Praveen, 2020. "On booms that never bust: Ambiguity in experimental asset markets with bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 110(C).
    18. Qian Lin & Frank Riedel, 2021. "Optimal consumption and portfolio choice with ambiguous interest rates and volatility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(3), pages 1189-1202, April.
    19. Ramsden, Lewis & Papaioannou, Apostolos D., 2019. "Ruin probabilities under capital constraints," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 273-282.
    20. 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.

    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:gam:jmathe:v:12:y:2023:i:1:p:40-:d:1305815. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.