OPTIMAL RETENTION FOR COMBINATION OF REINSURANCE PROTECTION USING MULTIOBJECTIVE OPTIMIZATION

• Main Author: Hanifah, Wira
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/44379
• Institution: Institut Teknologi Bandung

The risks faced by an insurance company which manages several business lines are high. For that reason, an insurance company need to share it risks with a reinsurance company. There are a number of reinsurances contract types, some of which are combinations of the proportional and non-proportional types of reinsurance contracts. One of the criteria in determining an optimal reinsurance contract is the meanvariance criterion which optimizes either the mean or the variance using the method of Lagrange multipliers. In this thesis, both the mean and the variance are optimized simultaneously (multiobjective problem). A combination of reinsurance contracts may result in a complex function and the variance is not always a convex function. In this thesis, to make it relatively easier in nding an optimal solution, a metaheuristic approach is applied which does not require the function to be convex, does not demand that function to be dierentiable, and does not require an estimate of initial value. This thesis discussed a combination of a quota share and an excess of loss reinsurance contracts. The optimization process for an optimal retention level of such combination of reinsurance contracts are solved by using a Lagrange multipliers method and Bat Multiobjective Optimization Algorithm (MOBA). As a case study, the severity of claims is assumed to follow a log-normal distribution with parameters = 7:07 and = 2:52, while the frequency of claims is assumed to follow a Poisson distribution with parameter = 330. To determine the reinsurance premium, that is the premium need to be paid by the insurance company to the reinsurance company, the expected value principle is used. We set the loading factor for the quota share reinsurance equals to q = 0:125, while that for the excess of loss equals to x = 0:3. It is obtained that the relative errors of 10 reinsurance optimal parameter values produced by the method of Lagrange and MOBA are less than 5%.