TY - GEN
T1 - Optimal reinsurance combination of quota-share and stop-loss reinsurance based on conditional-tail-expectation (CTE) optimization
AU - Orvin, Y.
AU - Nurrohmah, S.
AU - Fithriani, I.
N1 - Funding Information:
The Authors wishing to acknowledge assistance from various parties, including Faculty of Mathematics and Natural Science of Universitas Indonesia, teachers, and colleagues, in the making proccess of this paper. This work is supported by Hibah PUTI Prosiding 2020 funded by DRPM Universitas Indonesia No. NKB-994/UN2.RST/HKP.05.00/2020.
Publisher Copyright:
© 2021 Author(s).
PY - 2021/7/23
Y1 - 2021/7/23
N2 - To maintain financial stability and to effectively manage risk, an insurer will partially reinsure the loss to a reinsurance company. Two of the most often used reinsurance contracts are quota-share and stop-loss. In quota-share, the loss will be split based on a fixed proportion and the reinsurance premium depends on the value of the proportion, while in stop-loss the loss will be split depending on the retention value. In the hope that these two types of reinsurance can cover each other weaknesses, this study combines both quota-share and stop-loss reinsurance. Subsequently, to get a good coverage for the insurer, it is necessary to find the optimal proportion and retention value. One way to do so is using risk measure optimization. The smaller the value of the risk measure, the smaller the loss borne by the insurer. The risk measure used in this paper is Conditional-Tail-Expectation (CTE), where it involves Value-at-Risk (VaR) in its calculation. Calculated using the expected value principle, the reinsurance premium is used as a constraint in the CTE optimization for each of the reinsurance combinations, which are stop-loss after quota-share and quota-share after stop-loss. By optimizing CTE, it is found that each combination produces the same minimal CTE, so both reinsurance combinations are optimal for use by the insurer. By using different distributions, it is seen that the minimal CTE depends on the distribution's tail behavior. Furthermore, in determining the minimal value, the conditions that are used in optimization using CTE are different from VaR.
AB - To maintain financial stability and to effectively manage risk, an insurer will partially reinsure the loss to a reinsurance company. Two of the most often used reinsurance contracts are quota-share and stop-loss. In quota-share, the loss will be split based on a fixed proportion and the reinsurance premium depends on the value of the proportion, while in stop-loss the loss will be split depending on the retention value. In the hope that these two types of reinsurance can cover each other weaknesses, this study combines both quota-share and stop-loss reinsurance. Subsequently, to get a good coverage for the insurer, it is necessary to find the optimal proportion and retention value. One way to do so is using risk measure optimization. The smaller the value of the risk measure, the smaller the loss borne by the insurer. The risk measure used in this paper is Conditional-Tail-Expectation (CTE), where it involves Value-at-Risk (VaR) in its calculation. Calculated using the expected value principle, the reinsurance premium is used as a constraint in the CTE optimization for each of the reinsurance combinations, which are stop-loss after quota-share and quota-share after stop-loss. By optimizing CTE, it is found that each combination produces the same minimal CTE, so both reinsurance combinations are optimal for use by the insurer. By using different distributions, it is seen that the minimal CTE depends on the distribution's tail behavior. Furthermore, in determining the minimal value, the conditions that are used in optimization using CTE are different from VaR.
KW - Expected value principle
KW - quota-share reinsurance
KW - reinsurance premium
KW - stop-loss reinsurance
KW - value-at-risk (VaR)
UR - http://www.scopus.com/inward/record.url?scp=85112029919&partnerID=8YFLogxK
U2 - 10.1063/5.0059048
DO - 10.1063/5.0059048
M3 - Conference contribution
AN - SCOPUS:85112029919
T3 - AIP Conference Proceedings
BT - Proceedings of the 6th International Symposium on Current Progress in Mathematics and Sciences 2020, ISCPMS 2020
A2 - Ivandini, Tribidasari A.
A2 - Churchill, David G.
A2 - Lee, Youngil
A2 - Alias, Yatimah Binti
A2 - Margules, Chris
PB - American Institute of Physics Inc.
T2 - 6th International Symposium on Current Progress in Mathematics and Sciences 2020, ISCPMS 2020
Y2 - 27 October 2020 through 28 October 2020
ER -