JFRM  Vol.9 No.3 , September 2020
Optimal Insurance under Heterogeneous Belief
Abstract: In this paper, we study an optimal insurance problem, which allows the insured and the insurer to have heterogeneous probability beliefs in the distribution of potential losses, on the basis of which we maximize the expected utility of the insured’s final wealth. In order to reduce ex-post moral hazard, we assume that the alternative insurance contract follows the principle of indemnity and incentive compatibility constraints. Under the assumption of Wang’s premium principle, we derive a necessary and sufficient condition for the optimal solution. Then we discuss some particular characteristics of the optimal solution and the optimality of no insurance and full insurance.
Cite this paper: Yu, H. and Fang, Y. (2020) Optimal Insurance under Heterogeneous Belief. Journal of Financial Risk Management, 9, 179-189. doi: 10.4236/jfrm.2020.93010.

[1]   Arrow, K. J. (1963). Uncertainty and Welfare Economics of Medical Care. The American Economic Review, 53, 941-973.

[2]   Boonen, T. J. (2016). Optimal Reinsurance with Heterogeneous Reference Probabilities. Risks, 4, 26.

[3]   Cai, J., & Tan, K. S. (2007). Optimal Retention for a Stop-Loss Reinsurance under the VaR and CTE Risk Measures. ASTIN Bulletin, 37, 93-112.

[4]   Cheung, K. C. (2010). Optimal Reinsurance Revisited—A Geometric Approach. ASTIN Bulletin, 40, 221-239.

[5]   Chi, Y. (2019). On the Optimality of a Straight Deductible under Belief Heterogeneity. ASTIN Bulletin, 49, 242-263.

[6]   Chi, Y., & Lin, X. S. (2014). Optimal Reinsurance with Limited Ceded Risk: A Stochastic Dominance Approach. ASTIN Bulletin, 44, 103-126.

[7]   Chi, Y., & Zhuang, S. C. (2020). Optimal Insurance with Belief Heterogeneity and Incentive Compatibility. Insurance: Mathematics and Economics, 92, 104-114.

[8]   Ghossoub, M. (2016). Optimal Insurance with Heterogeneous Beliefs and Disagreement about Zero-Probability Events. Risks, 4, 29.

[9]   Ghossoub, M. (2017). Arrow’s Theorem of the Deductible with Heterogeneous Beliefs. North American Actuarial Journal, 21, 15-35.

[10]   Gollier, C. (2013). The Economics of Optimal Insurance Design. In G. Dionne (Ed.), Handbook of Insurance (2nd ed., pp. 107-122). New York: Springer.

[11]   Huberman, G., Mayers, D., & Smith Jr., C. W. (1983). Optimal Insurance Policy Indemnity Schedules. The Bell Journal of Economics, 14, 415-426.

[12]   Jiang, W., Ren, J., Yang, C., & Hong, H. (2019). On Optimal Reinsurance Treaties in Cooperative Game under Heterogeneous Beliefs. Insurance: Mathematics and Economics, 85, 173-184.

[13]   Liu, Z. B., Zhao, R. Q., Liu, X. Y., & Chen, L. (2017). Contract Designing for a Supply Chain with Uncertain Information Based on Confidence Level. Applied Soft Computing, 56, 617-631.

[14]   Marshall, J. (1992). Optimum Insurance with Deviant Beliefs. In G. Dionne (Ed.), Contributions to Insurance Economics (pp. 255-274). Boston, MA: Kluwer Academic Publishers.

[15]   Savage, L. J. (1972). The Foundations of Statistics (2nd revised ed.). New York: Dover Publications, Inc.

[16]   Smith, V. L. (1968). Optimal Insurance Coverage. Journal of Political Economy, 76, 68-77.

[17]   Xu, Z. Q., Zhou, X. Y. & Zhuang, S. C. (2019). Optimal Insurance with Rank-Dependent Utility and Incentive Compatibility. Mathematical Finance, 29, 659-692.

[18]   Young, V. R. (1999). Optimal Insurance under Wang’s Premium Principle. Insurance: Mathematics and Economics, 25, 109-122.