Quota-share and stop-loss reinsurance combination based on Value-at-Risk (VaR) optimization

Abstract

Every insurance companies have a capacity limit related to the maximum claim that can be borne. Therefore, insurance companies need to reinsure risks to reinsurance companies. Besides of quota-share, types of reinsurance contracts that commonly used is stop-loss. The quota-share reinsurance premium is proportional based on the amount claim that is covered, but not safe against a large claim. While for stop-loss, the reinsurance premium is relatively large but safe for a large claim. So, this paper combines both types of reinsurance to cover the shortcomings with their respective strengths. After being combined, it is necessary to determine the optimal quota-share proportion and stop-loss retention. One criterion of determines optimal proportion and retention is based on Value-at-Risk (VaR) optimization. With the reinsurance premium as a constraint, this optimization problem is solved for each type of reinsurance combination, be it quota-share before stop-loss or stop-loss before quota-share. From each of these types combinations, the result is optimal quota-share proportion and stop-loss retention, so as produce a minimum VaR value from the borne risk by insurance companies. by comparing the results of VaR optimization of these combinations, stop-loss before quota-share is obtained resulting in a more minimum VaR value.