OPTIMAL RETENTION FOR COMBINATION OF REINSURANCE PROTECTION USING MULTIOBJECTIVE OPTIMIZATION
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-proportiona...
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Format: | Theses |
Language: | Indonesia |
Online Access: | https://digilib.itb.ac.id/gdl/view/44379 |
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Institution: | Institut Teknologi Bandung |
Language: | Indonesia |
Summary: | 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%. |
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