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Risk-adjusted Bowley reinsurance under distorted probabilities

Ka Chun Cheung, Sheung Chi Phillip Yam and Yiying Zhang

Insurance: Mathematics and Economics, 2019, vol. 86, issue C, 64-72

Abstract: In the seminal work of Chan and Gerber (1985), one of the earliest game theoretical approaches was proposed to model the interaction between the reinsurer and insurer; in particular, the optimal pricing density for the reinsurer and optimal ceded loss for the insurer were determined so that their corresponding expected utilities could be maximized. Over decades, their advocated Bowley solution (could be understood as Stackelberg equilibria) concept of equilibrium reinsurance strategy has not been revisited in the modern risk management framework. In this article, we attempt to fill this gap by extending their work to the setting of general premium principle for the reinsurer and distortion risk measure for the insurer.

Keywords: Bowley solution; Stackelberg equilibria; Equilibrium reinsurance strategy; Pricing density; General premium principle; Distortion risk measure; Tail Value-at-Risk; Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C61 G22 G32 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.insmatheco.2019.02.006

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