Optimal reinsurance using the expected shortfall

The Financial Services Authority Regulation regarding Self-Retention and Domestic Reinsurance Support (Otoritas Jasa Keuangan / OJK Regulation) was issued to establish a more comprehensive framework concerning self-retention and reinsurance support of insurance companies. Insurance Companies must implement and maintain a self-retention limit based on their risk and loss profile. This requires Insurance Companies to make available a certain amount of capital for every risk that they undertake. Insurance companies must develop and implement a reinsurance support strategy to ensure that they have sufficient capacity to meet their liabilities. In this research, we estimate the optimal retention by means of Expected Shortfall which will minimize the risk of individual total based on the quota share reinsurance. We use lognormal bivariate distribution to illustrate the optimal retention in an individual risk model.