IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v95y2020icp17-27.html
   My bibliography  Save this article

Pareto-optimal insurance contracts with premium budget and minimum charge constraints

Author

Listed:
  • Asimit, Alexandru V.
  • Cheung, Ka Chun
  • Chong, Wing Fung
  • Hu, Junlei

Abstract

In view of the fact that minimum charge and premium budget constraints are natural economic considerations in any risk-transfer between the insurance buyer and seller, this paper revisits the optimal insurance contract design problem in terms of Pareto optimality with imposing these practical constraints. Pareto optimal insurance contracts, with indemnity schedule and premium payment, are solved in the cases when the risk preferences of the buyer and seller are given by Value-at-Risk or Tail Value-at-Risk. The effect of our constraints and the relative bargaining powers of the buyer and seller on the Pareto optimal insurance contracts are highlighted. Numerical experiments are employed to further examine these effects for some given risk preferences.

Suggested Citation

  • Asimit, Alexandru V. & Cheung, Ka Chun & Chong, Wing Fung & Hu, Junlei, 2020. "Pareto-optimal insurance contracts with premium budget and minimum charge constraints," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 17-27.
    • Handle: RePEc:eee:insuma:v:95:y:2020:i:c:p:17-27
    DOI: 10.1016/j.insmatheco.2020.08.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720301128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.08.001?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. Chi, Yichun, 2019. "On The Optimality Of A Straight Deductible Under Belief Heterogeneity," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 243-262, January.
    2. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "The optimal insurance under disappointment theories," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 77-90.
    3. Carole Bernard & Xuedong He & Jia-An Yan & Xun Yu Zhou, 2015. "Optimal Insurance Design Under Rank-Dependent Expected Utility," Mathematical Finance, Wiley Blackwell, vol. 25(1), pages 154-186, January.
    4. Gur Huberman & David Mayers & Clifford W. Smith Jr., 1983. "Optimal Insurance Policy Indemnity Schedules," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 415-426, Autumn.
    5. Cui, Wei & Yang, Jingping & Wu, Lan, 2013. "Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 74-85.
    6. Alexandru V. Asimit & Tao Gao & Junlei Hu & Eun-Seok Kim, 2018. "Optimal Risk Transfer: A Numerical Optimization Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 22(3), pages 341-364, July.
    7. Ken Seng Tan & Chengguo Weng, 2014. "Empirical Approach for Optimal Reinsurance Design," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(2), pages 315-342, April.
    8. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance with belief heterogeneity," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 79-91.
    9. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.
    10. Ambrose Lo & Zhaofeng Tang, 2019. "Pareto-optimal reinsurance policies in the presence of individual risk constraints," Annals of Operations Research, Springer, vol. 274(1), pages 395-423, March.
    11. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    12. Cai, Jun & Lemieux, Christiane & Liu, Fangda, 2016. "Optimal Reinsurance From The Perspectives Of Both An Insurer And A Reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 815-849, September.
    13. Asimit, Alexandru V. & Hu, Junlei & Xie, Yuantao, 2019. "Optimal robust insurance with a finite uncertainty set," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 67-81.
    14. Lo, Ambrose, 2017. "A Neyman-Pearson Perspective On Optimal Reinsurance With Constraints," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 467-499, May.
    15. Zuo Quan Xu & Xun Yu Zhou & Sheng Chao Zhuang, 2019. "Optimal insurance under rank‐dependent utility and incentive compatibility," Mathematical Finance, Wiley Blackwell, vol. 29(2), pages 659-692, April.
    16. Chi, Yichun & Liu, Fangda, 2017. "Optimal insurance design in the presence of exclusion clauses," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 185-195.
    17. Asimit, Alexandru V. & Bignozzi, Valeria & Cheung, Ka Chun & Hu, Junlei & Kim, Eun-Seok, 2017. "Robust and Pareto optimality of insurance contracts," European Journal of Operational Research, Elsevier, vol. 262(2), pages 720-732.
    18. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    19. Cai, Jun & Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2008. "Optimal reinsurance under VaR and CTE risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 185-196, August.
    20. Tan, Ken Seng & Weng, Chengguo & Zhang, Yi, 2011. "Optimality of general reinsurance contracts under CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 175-187, September.
    21. Chi, Yichun, 2012. "Reinsurance Arrangements Minimizing the Risk-Adjusted Value of an Insurer's Liability," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 529-557, November.
    22. Zhuang, Sheng Chao & Weng, Chengguo & Tan, Ken Seng & Assa, Hirbod, 2016. "Marginal Indemnification Function formulation for optimal reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 65-76.
    23. Zheng, Yanting & Cui, Wei, 2014. "Optimal reinsurance with premium constraint under distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 109-120.
    24. Sung, K.C.J. & Yam, S.C.P. & Yung, S.P. & Zhou, J.H., 2011. "Behavioral optimal insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 418-428.
    25. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    26. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    27. Cai, Jun & Liu, Haiyan & Wang, Ruodu, 2017. "Pareto-optimal reinsurance arrangements under general model settings," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 24-37.
    28. Boonen, Tim J. & Ghossoub, Mario, 2019. "On the existence of a representative reinsurer under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 209-225.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Asimit, Alexandru V. & Boonen, Tim J. & Chi, Yichun & Chong, Wing Fung, 2021. "Risk sharing with multiple indemnity environments," European Journal of Operational Research, Elsevier, vol. 295(2), pages 587-603.

    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. Jiang, Wenjun & Hong, Hanping & Ren, Jiandong, 2021. "Pareto-optimal reinsurance policies with maximal synergy," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 185-198.
    2. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    3. Chi, Yichun & Zhuang, Sheng Chao, 2020. "Optimal insurance with belief heterogeneity and incentive compatibility," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 104-114.
    4. Asimit, Alexandru V. & Boonen, Tim J. & Chi, Yichun & Chong, Wing Fung, 2021. "Risk sharing with multiple indemnity environments," European Journal of Operational Research, Elsevier, vol. 295(2), pages 587-603.
    5. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2020. "Optimal Insurance under Maxmin Expected Utility," Papers 2010.07383, arXiv.org.
    6. Boonen, Tim J. & Jiang, Wenjun, 2022. "A marginal indemnity function approach to optimal reinsurance under the Vajda condition," European Journal of Operational Research, Elsevier, vol. 303(2), pages 928-944.
    7. Boonen, Tim J. & Ghossoub, Mario, 2021. "Optimal reinsurance with multiple reinsurers: Distortion risk measures, distortion premium principles, and heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 23-37.
    8. Cheung, Ka Chun & Phillip Yam, Sheung Chi & Yuen, Fei Lung & Zhang, Yiying, 2020. "Concave distortion risk minimizing reinsurance design under adverse selection," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 155-165.
    9. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance without the nonnegativity constraint on indemnities," Insurance: Mathematics and Economics, Elsevier, vol. 84(C), pages 22-39.
    10. Ghossoub, Mario, 2019. "Budget-constrained optimal insurance with belief heterogeneity," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 79-91.
    11. Boonen, Tim J. & Ghossoub, Mario, 2019. "On the existence of a representative reinsurer under heterogeneous beliefs," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 209-225.
    12. Boonen, Tim J. & Jiang, Wenjun, 2022. "Bilateral risk sharing in a comonotone market with rank-dependent utilities," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 361-378.
    13. Lu, Zhiyi & Meng, Shengwang & Liu, Leping & Han, Ziqi, 2018. "Optimal insurance design under background risk with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 80(C), pages 15-28.
    14. Ghossoub, Mario & Jiang, Wenjun & Ren, Jiandong, 2022. "Pareto-optimal reinsurance under individual risk constraints," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 307-325.
    15. Asimit, Alexandru V. & Hu, Junlei & Xie, Yuantao, 2019. "Optimal robust insurance with a finite uncertainty set," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 67-81.
    16. Liang, Xiaoqing & Jiang, Wenjun & Zhang, Yiying, 2023. "Optimal insurance design under mean-variance preference with narrow framing," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 59-79.
    17. Ghossoub, Mario & He, Xue Dong, 2021. "Comparative risk aversion in RDEU with applications to optimal underwriting of securities issuance," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 6-22.
    18. Asimit, Vali & Boonen, Tim J., 2018. "Insurance with multiple insurers: A game-theoretic approach," European Journal of Operational Research, Elsevier, vol. 267(2), pages 778-790.
    19. Ambrose Lo & Zhaofeng Tang, 2019. "Pareto-optimal reinsurance policies in the presence of individual risk constraints," Annals of Operations Research, Springer, vol. 274(1), pages 395-423, March.
    20. Cheung, K.C. & Chong, W.F. & Yam, S.C.P., 2015. "Convex ordering for insurance preferences," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 409-416.

    More about this item

    Keywords

    Bargaining power; Minimum charge; Optimal insurance contract design; Pareto optimality; Premium budget; Proportional Hazard Transformation; Tail Value-at-Risk; Value-at-Risk;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:insuma:v:95:y:2020:i:c:p:17-27. 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/locate/inca/505554 .

    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.