Optimal reinsurance design under the VaR risk measure and asymmetric information

Yuchen Yuan; Ying Fang; Yuchen Yuan; Ying Fang

doi:10.3934/mmc.2022017

Mathematical Modelling and Control

2022, Volume 2, Issue 4: 165-175. doi: 10.3934/mmc.2022017

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Research article

Optimal reinsurance design under the VaR risk measure and asymmetric information

Yuchen Yuan ^,,
Ying Fang

School of Mathematics and Statistics, Shandong Normal University, Jinan, 250358, Shandong, China

Received: 24 July 2022 Revised: 14 September 2022 Accepted: 30 October 2022 Published: 16 December 2022

This paper analyzes a monopoly reinsurance market in the presence of asymmetric information. Insurers use Value-at-Risk measures to quantify their risks and have different risk exposures and risk preferences, but the type of each insurer is hidden information to the reinsurer. The reinsurer maximizes the expected profit under the constraint of incentive compatibility and individual rationality. We deduce the optimal reinsurance menu under the assumption that a type of insurer thinks he is at greater risks. Some comparative analyses are given for two strategies of separating equilibrium and pooling equilibrium.
- optimal insurance,
- value-at-risk,
- asymmetric information,
- separating equilibrium,
- pooling equilibrium
Citation: Yuchen Yuan, Ying Fang. Optimal reinsurance design under the VaR risk measure and asymmetric information[J]. Mathematical Modelling and Control, 2022, 2(4): 165-175. doi: 10.3934/mmc.2022017

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Abstract

This paper analyzes a monopoly reinsurance market in the presence of asymmetric information. Insurers use Value-at-Risk measures to quantify their risks and have different risk exposures and risk preferences, but the type of each insurer is hidden information to the reinsurer. The reinsurer maximizes the expected profit under the constraint of incentive compatibility and individual rationality. We deduce the optimal reinsurance menu under the assumption that a type of insurer thinks he is at greater risks. Some comparative analyses are given for two strategies of separating equilibrium and pooling equilibrium.

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