Optimal Retention for a Quota Share Reinsurance

The Indonesian Financial Services Authority (OJK) has instructed all insurance providers in Indonesia to apply a mandatory tariff for property insurance. The tariff has to be uniformly applied and the rule to set the maximum and minimum premium rates for protection against losses should be applied. Furthermore, the OJK issued the new rule regarding self- retention and domestic reinsurance. Insurance companies are obliged to have and implement self-retention for each risk in accordance with the self-retention limits. Fluctuations in total premium income and claims may lead the insurance company cannot fulfill the obligation to the insured, thus the company needs to conduct reinsurance. Reinsurance helps protect insurers against unforeseen or extraordinary losses by allowing them to spread their risks. Since reinsurer chargers premium to the insurance company, a properly calculated optimal retention would be nearly as high as the insurer financial ability. This paper is aimed at determining optimal retentions indicated by the risk measure Value at Risk (VaR), Expected Shortfall (ES) and Minimum Variance (MV). Here we use the expectation premium principle which minimizes individual risks based on their quota share reinsurance. Regarding the data in an insurance property, we use a bivariate lognormal (BLN) distribution to obtain VaR, ES, and MV, and a bivariate exponential (BEXP) distribution to obtain MV. The bivariate distributions are required to derive the conditional probability of the amount of claim occurs given the benefit has occurred. We find that first, based on fitting distribution, the use of bivariate lognormal distribution is suitable for the determination of retention and the value of MV is between VaR and ES. Second, the value of MV-BEXP is less than MV-BLN that have an impact on high reinsurance„s value.