Optimal Retention for a Quota-Share Reinsurance

Lienda Noviyanti, Achmad Zanbar Soleh, Anna Chadidjah, Hasna Afifah Rusyda


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 of set the maximum and minimum premium rates for protection against losses. 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 of total premium income and claims may lead the insurance company cannot fulfil 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. Because 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 to the data in an insurance property, we use a bivariate lognormal distribution to obtain VaR, ES and MV, and a bivariate exponential 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.


Property Quota Share Insurance Optimal Retention; Minimum Variance; Value at Risk; Expected Shortfall; Bivariate Lognormal Distribution; Bivariate Exponential Distribution

Full Text:



Acerbi, C., dan Tasche, D. (2002). On the Coherence of Expected Shortfall. Journal of Banking and Finance, 26, pp. 1487-1503.

Balbas, A., Balbas, B., Heras, A. (2010). Stability of the Optimal Reinsurance with Respect to the Risk Measure. Working Paper 10-02. Business Economic Series 01.

Borch, K. (1960). An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance. Transaction of the 16th International Congress of Actuaries I. pp. 597–610.

Cai, J., and K. S. Tan, (2007). Optimal Retention for a Stop-Loss Reinsurance under the VaR and CTE Risk Measure. ASTIN Bulletin, 37 (1), pp. 93-112.

Cai, J. , Tan, K. S., Weng, C., and Zhang, Y. (2008) Optimal Reinsurance under the VaR and CTE Risk Measure. Insurance: Mathematics and Economics 43 (1), 185-196.

Kaluszka, M. (2001) Optimal Reinsurance under Mean-Variance premium Principles. Insurance: Mathematics and Economics 28, pp. 61-67.

Kaluszka, M. (2004) Mean-Variance Optimal Reinsurance Arrangements. Scandinavian Actuarial Journal I, pp. 28-41.

Noviyanti, L., Soleh, A.Z. and Chadidjah, A., presented at The International Conference on Mathematics, Science, Education and Technology, 2017.

Panjer, H. and Willmot, G. (1992). Insurance Risk Models. Chicago: Society of Actuaries.

Pressacco F., Serafini, I. and Ziani, L. 2010. Mean-Variance Efficient Strategies in Proportional Reinsurance under Group Correlation in a Gaussian Framework. Accepted for publication on European Actuarial Journal, first number.

Tan, K. S., Weng, C., and Zhang, Y. 2009. VaR and ES criteria for optimal quota-share and stop-loss reinsurance. North American Actuarial Journal 13 (4), pp. 459-482.

Soleh, A.Z., Noviyanti, L., Nurrahmawati, I., (2015). Retention for stop-loss reinsurance to minimize VaR in compound Poisson-Lognormal distribution. AIP Conf. Proc. 1692, 020026; 1.4936454


Instructions for Preparing Papers for JTI.docx
Panduan untuk Menulis di JTI.docx

The Journal is published by The Institute of Research & Community Outreach - Petra Christian University. It available online supported by Directorate General of Higher Education - Ministry of National Education - Republic of Indonesia.

©All right reserved 2016.Jurnal Teknik Industri, ISSN: 1411-2485, e-ISSN: 2087-7439

shopify traffic stats
View My Stats