IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp155-165.html
   My bibliography  Save this article

Concave distortion risk minimizing reinsurance design under adverse selection

Author

Listed:
  • Cheung, Ka Chun
  • Phillip Yam, Sheung Chi
  • Yuen, Fei Lung
  • Zhang, Yiying

Abstract

This article makes use of the well-known Principal–Agent (multidimensional screening) model commonly used in economics to analyze a monopolistic reinsurance market in the presence of adverse selection, where the risk preference of each insurer is guided by its concave distortion risk measure of the terminal wealth position; while the reinsurer, under information asymmetry, aims to maximize its expected profit by designing an optimal policy provision (menu) of “shirt-fit” stop-loss reinsurance contracts for every insurer of either type of low or high risk. In particular, the most representative case of Tail Value-at-Risk (TVaR) is further explored in detail so as to unveil the underlying insight from economics perspective.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:155-165
    DOI: 10.1016/j.insmatheco.2020.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300172
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.02.001?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. Neil Doherty & Kent Smetters, 2005. "Moral Hazard in Reinsurance Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(3), pages 375-391, September.
    2. Michel Mougeot & Florence Naegelen, 2009. "Moral Hazard, Adverse Selection and Outlier Payment Policy," Post-Print hal-00448965, HAL.
    3. Keith J. Crocker & Arthur Snow, 2011. "Multidimensional Screening in Insurance Markets with Adverse Selection," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 78(2), pages 287-307, June.
    4. Michel Mougeot & Florence Naegelen, 2009. "Adverse Selection, Moral Hazard, and Outlier Payment Policy," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(1), pages 177-195, March.
    5. Nathaniel Hendren, 2013. "Private Information and Insurance Rejections," Econometrica, Econometric Society, vol. 81(5), pages 1713-1762, September.
    6. David M. Cutler & Richard J. Zeckhauser, 1999. "Reinsurance for Catastrophes and Cataclysms," NBER Chapters, in: The Financing of Catastrophe Risk, pages 233-274, National Bureau of Economic Research, Inc.
    7. Martin Eling & Ruo Jia & Yi Yao, 2017. "Between-Group Adverse Selection: Evidence From Group Critical Illness Insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 771-809, June.
    8. Lesław Gajek & Dariusz Zagrodny, 2004. "Reinsurance Arrangements Maximizing Insurer's Survival Probability," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(3), pages 421-435, September.
    9. Guerra, Manuel & de Lourdes Centeno, Maria, 2008. "Optimal reinsurance policy: The adjustment coefficient and the expected utility criteria," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 529-539, April.
    10. Eling, Martin & Gatzert, Nadine & Schmeiser, Hato, 2009. "Minimum standards for investment performance: A new perspective on non-life insurer solvency," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 113-122, August.
    11. Kenneth A. Froot, 1999. "The Financing of Catastrophe Risk," NBER Books, National Bureau of Economic Research, Inc, number froo99-1.
    12. Barrieu, Pauline & Loubergé, Henri, 2013. "Reinsurance and securitisation of life insurance risk: The impact of regulatory constraints," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 135-144.
    13. Kaluszka, Marek, 2005. "Optimal reinsurance under convex principles of premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 375-398, June.
    14. Alejandro Balbás & José Garrido & Silvia Mayoral, 2009. "Properties of Distortion Risk Measures," Methodology and Computing in Applied Probability, Springer, vol. 11(3), pages 385-399, September.
    15. Mathieu Bargès & Hélène Cossette & Etienne Marceau, 2009. "TVaR-based capital allocation with copulas," Working Papers hal-00431265, HAL.
    16. Carlier, G. & Dana, R.-A., 2005. "Rearrangement inequalities in non-convex insurance models," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 483-503, August.
    17. Meglena Jeleva & Bertrand Villeneuve, 2004. "Insurance contracts with imprecise probabilities and adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(4), pages 777-794, May.
    18. repec:dau:papers:123456789/5358 is not listed on IDEAS
    19. Ryan Matthew Joseph & Vaithianathan Rhema, 2003. "Adverse Selection and Insurance Contracting: A Rank-Dependent Utility Analysis," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-20, August.
    20. Cheung, K.C. & Liu, F. & Yam, S.C.P., 2012. "Average Value-at-Risk Minimizing Reinsurance Under Wang's Premium Principle with Constraints," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 575-600, November.
    21. Alma Cohen & Peter Siegelman, 2010. "Testing for Adverse Selection in Insurance Markets," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(1), pages 39-84, March.
    22. repec:dau:papers:123456789/5389 is not listed on IDEAS
    23. Peng Shi & Wei Zhang & Emiliano A. Valdez, 2012. "Testing Adverse Selection With Two-Dimensional Information: Evidence From the Singapore Auto Insurance Market," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 79(4), pages 1077-1114, December.
    24. Georges Dionne (ed.), 2013. "Handbook of Insurance," Springer Books, Springer, edition 2, number 978-1-4614-0155-1, June.
    25. Joseph E. Stiglitz, 1977. "Monopoly, Non-linear Pricing and Imperfect Information: The Insurance Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 44(3), pages 407-430.
    26. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    27. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    28. , & ,, 2012. "Optimal insurance with adverse selection," Theoretical Economics, Econometric Society, vol. 7(3), September.
    29. 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.
    30. 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.
    31. Michael Landsberger & Isaac Meilijson, 1999. "A general model of insurance under adverse selection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 331-352.
    32. K. C. Cheung & K. C. J. Sung & S. C. P. Yam, 2014. "Risk-Minimizing Reinsurance Protection For Multivariate Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(1), pages 219-236, March.
    33. 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.
    34. Assa, Hirbod, 2015. "On optimal reinsurance policy with distortion risk measures and premiums," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 70-75.
    35. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    36. 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.
    37. Tsanakas, Andreas, 2004. "Dynamic capital allocation with distortion risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 223-243, October.
    38. 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.
    39. 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.
    40. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    41. Bargès, Mathieu & Cossette, Hélène & Marceau, Étienne, 2009. "TVaR-based capital allocation with copulas," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 348-361, December.
    42. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2011. "Stable solutions for optimal reinsurance problems involving risk measures," European Journal of Operational Research, Elsevier, vol. 214(3), pages 796-804, November.
    43. Raviv, Artur, 1979. "The Design of an Optimal Insurance Policy," American Economic Review, American Economic Association, vol. 69(1), pages 84-96, March.
    44. Virginia R. Young & Mark J. Browne, 2000. "Equilibrium in Competitive Insurance Markets Under Adverse Selection and Yaari's Dual Theory of Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 25(2), pages 141-157, December.
    45. Balbás, Alejandro & Balbás, Beatriz & Heras, Antonio, 2009. "Optimal reinsurance with general risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 374-384, June.
    46. Jun Cai & Ying Fang & Zhi Li & Gordon E. Willmot, 2013. "Optimal Reciprocal Reinsurance Treaties Under the Joint Survival Probability and the Joint Profitable Probability," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(1), pages 145-168, March.
    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. Wakker, Peter P. & Yang, Jingni, 2021. "Concave/convex weighting and utility functions for risk: A new light on classical theorems," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 429-435.
    2. Liu, Haiyan, 2024. "Worst-case risk with unspecified risk preferences," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 235-248.

    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. Cheung, Ka Chun & Yam, Sheung Chi Phillip & Zhang, Yiying, 2019. "Risk-adjusted Bowley reinsurance under distorted probabilities," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 64-72.
    2. Mi Chen & Wenyuan Wang & Ruixing Ming, 2016. "Optimal Reinsurance Under General Law-Invariant Convex Risk Measure and TVaR Premium Principle," Risks, MDPI, vol. 4(4), pages 1-12, December.
    3. 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.
    4. 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.
    5. Cheung, Ka Chun & He, Wanting & Wang, He, 2023. "Multi-constrained optimal reinsurance model from the duality perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 199-214.
    6. 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.
    7. Guerra, Manuel & Centeno, M.L., 2012. "Are quantile risk measures suitable for risk-transfer decisions?," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 446-461.
    8. Yuxia Huang & Chuancun Yin, 2018. "A unifying approach to constrained and unconstrained optimal reinsurance," Papers 1807.06892, arXiv.org.
    9. Boonen, Tim J. & Jiang, Wenjun, 2024. "Robust insurance design with distortion risk measures," European Journal of Operational Research, Elsevier, vol. 316(2), pages 694-706.
    10. 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.
    11. Ghossoub, Mario, 2019. "Optimal insurance under rank-dependent expected utility," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 51-66.
    12. Boonen, Tim J. & Tan, Ken Seng & Zhuang, Sheng Chao, 2021. "Optimal reinsurance with multiple reinsurers: Competitive pricing and coalition stability," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 302-319.
    13. Ghossoub, Mario & Zhu, Michael B., 2024. "Stackelberg equilibria with multiple policyholders," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 189-201.
    14. Lu, ZhiYi & Meng, LiLi & Wang, Yujin & Shen, Qingjie, 2016. "Optimal reinsurance under VaR and TVaR risk measures in the presence of reinsurer’s risk limit," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 92-100.
    15. Alejandro Balbas & Beatriz Balbas & Raquel Balbas, 2013. "Optimal Reinsurance: A Risk Sharing Approach," Risks, MDPI, vol. 1(2), pages 1-12, August.
    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. 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.
    18. Attar, Andrea & Mariotti, Thomas & Salanié, François, 2014. "Multiple Contracting in Insurance Markets," IDEI Working Papers 839, Institut d'Économie Industrielle (IDEI), Toulouse, revised Sep 2016.
    19. Dionne, Georges & Harrington, Scott, 2017. "Insurance and Insurance Markets," Working Papers 17-2, HEC Montreal, Canada Research Chair in Risk Management.
    20. 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.

    More about this item

    Keywords

    Risk management; Principal–agent problem; Distortion risk measure; Incentive compatibility; Individual rationality;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:91:y:2020:i:c:p:155-165. 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.