Optimal insurance design under asymmetric Nash bargaining

Yichun Chi, Tao Hu, Zhengtang Zhao and Jiakun Zheng
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Yichun Chi: Central University of Finance and Economics [Beijing]
Tao Hu: University of Oulu [Finland] = Oulun yliopisto [Suomi] = Université d'Oulu [Finlande]
Jiakun Zheng: Renmin University of China = Université Renmin de Chine, China Financial Policy Research Center - Renmin University of China = Université Renmin de Chine, AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, AMU - Aix Marseille Université

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Abstract: This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. Under asymmetric Nash bargaining, we show that the Pareto-optimal insurance contract always contains a straight deductible under linear transaction costs and that the deductible disappears if and only if the deadweight cost is zero, regardless of the insurer's bargaining power. We further find that the optimality of no insurance is consistent across all market structures. When the insured's risk preference exhibits decreasing absolute risk aversion, the optimal deductible and the insurer's expected loss decrease in the degree of the insured's risk aversion and thus increase in the insured's initial wealth. In addition, the effect of increasing the insurer's bargaining power on the optimal deductible is equivalent to a pure effect of reducing the initial wealth of the insured. Our results suggest that the well-documented preference for low deductibles could be the result of insurance bargaining.

Keywords: Asymmetric Nash bargaining; Risk sharing; Deductible insurance; Wealth effect; Overinsurance (search for similar items in EconPapers)
Date: 2024-11
Note: View the original document on HAL open archive server: https://hal.science/hal-04718332v1
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Published in Insurance: Mathematics and Economics, 2024, 119, pp.194-209. ⟨10.1016/j.insmatheco.2024.08.006⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04718332

DOI: 10.1016/j.insmatheco.2024.08.006

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