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Optimal insurance with information asymmetry: Nonlinear and linear pricing

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  • Han, Xia
  • Li, Bin
  • Luo, Yao

Abstract

We propose a new framework for studying optimal insurance under information asymmetry within the Stackelberg game framework. In this setting, a monopolistic insurer faces uncertainty regarding a customer’s loss distribution or risk attitude. The customer is assumed to follow a mean-variance preference in continuous time, while the insurer sets premiums through a risk loading based on the expected loss. An optimal menu is explicitly derived for a general class of aggregate loss models.

Suggested Citation

  • Han, Xia & Li, Bin & Luo, Yao, 2026. "Optimal insurance with information asymmetry: Nonlinear and linear pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:dyncon:v:184:y:2026:i:c:s0165188926000114
    DOI: 10.1016/j.jedc.2026.105265
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    References listed on IDEAS

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    1. Jaeyoung Sung, 2005. "Optimal Contracts Under Adverse Selection and Moral Hazard: A Continuous-Time Approach," The Review of Financial Studies, Society for Financial Studies, vol. 18(3), pages 1021-1073.
    2. Chen, Lv & Shen, Yang, 2018. "On A New Paradigm Of Optimal Reinsurance: A Stochastic Stackelberg Differential Game Between An Insurer And A Reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 905-960, May.
    3. 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.
    4. Li, Bin & Li, Danping & Xiong, Dewen, 2016. "Alpha-robust mean-variance reinsurance-investment strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 70(C), pages 101-123.
    5. 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.
    6. Puelz, Robert & Snow, Arthur, 1994. "Evidence on Adverse Selection: Equilibrium Signaling and Cross-Subsidization in the Insurance Market," Journal of Political Economy, University of Chicago Press, vol. 102(2), pages 236-257, April.
    7. 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.
    8. , & ,, 2012. "Optimal insurance with adverse selection," Theoretical Economics, Econometric Society, vol. 7(3), September.
    9. Nathaniel Hendren, 2013. "Private Information and Insurance Rejections," Econometrica, Econometric Society, vol. 81(5), pages 1713-1762, September.
    10. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random losses and Adverse Selection," CRC TR 224 Discussion Paper Series crctr224_2023_399, University of Bonn and University of Mannheim, Germany.
    11. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    12. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    13. Min Dai & Hanqing Jin & Steven Kou & Yuhong Xu, 2021. "A Dynamic Mean-Variance Analysis for Log Returns," Management Science, INFORMS, vol. 67(2), pages 1093-1108, February.
    14. Jakša Cvitanić & Dylan Possamaï & Nizar Touzi, 2017. "Moral Hazard in Dynamic Risk Management," Management Science, INFORMS, vol. 63(10), pages 3328-3346, October.
    15. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    16. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random Losses and Adverse Selection," ECONtribute Discussion Papers Series 242, University of Bonn and University of Cologne, Germany.
    17. Alex Gershkov & Benny Moldovanu & Philipp Strack & Mengxi Zhang, 2023. "Optimal Insurance: Dual Utility, Random Losses, and Adverse Selection," American Economic Review, American Economic Association, vol. 113(10), pages 2581-2614, October.
    18. Tomas Philipson & John Cawley, 1999. "An Empirical Examination of Information Barriers to Trade in Insurance," American Economic Review, American Economic Association, vol. 89(4), pages 827-846, September.
    19. Guan, Guohui & Li, Bin, 2022. "Equilibrium investment and reinsurance strategies under smooth ambiguity with a general second-order distribution," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    20. Christian Gollier, 2014. "Optimal insurance design of ambiguous risks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(3), pages 555-576, November.
    21. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    22. Jakša Cvitanić & Xuhu Wan & Huali Yang, 2013. "Dynamics of Contract Design with Screening," Management Science, INFORMS, vol. 59(5), pages 1229-1244, May.
    23. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    24. Garcia, Daniel & Tsur, Matan, 2021. "Information design in competitive insurance markets," Journal of Economic Theory, Elsevier, vol. 191(C).
    25. Alma Cohen & Liran Einav, 2007. "Estimating Risk Preferences from Deductible Choice," American Economic Review, American Economic Association, vol. 97(3), pages 745-788, June.
    26. Amy Finkelstein & Kathleen McGarry, 2006. "Multiple Dimensions of Private Information: Evidence from the Long-Term Care Insurance Market," American Economic Review, American Economic Association, vol. 96(4), pages 938-958, September.
    27. Vitor Farinha Luz & Piero Gottardi & Humberto Moreira, 2023. "Risk Classification in Insurance Markets with Risk and Preference Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 3022-3082.
    28. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    29. Chade, Hector & Schlee, Edward E., 2020. "Insurance as a lemons market: Coverage denials and pooling," Journal of Economic Theory, Elsevier, vol. 189(C).
    30. Suleyman Basak & Georgy Chabakauri, 2010. "Dynamic Mean-Variance Asset Allocation," The Review of Financial Studies, Society for Financial Studies, vol. 23(8), pages 2970-3016, August.
    31. Yuan-Mao Kao & N. Bora Keskin & Kevin Shang, 2022. "Impact of Information Asymmetry and Limited Production Capacity on Business Interruption Insurance," Management Science, INFORMS, vol. 68(4), pages 2824-2841, April.
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    Cited by:

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