Optimal reinsurance design under the VaR risk measure and asymmetric information

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.