IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v10y2017i1p4-d88747.html
   My bibliography  Save this article

Determination of the Optimal Retention Level Based on Different Measures

Author

Listed:
  • Başak Bulut Karageyik

    (Department of Actuarial Sciences, Hacettepe University, 06800 Ankara, Turkey)

  • Şule Şahin

    (Department of Actuarial Sciences, Hacettepe University, 06800 Ankara, Turkey)

Abstract

This paper deals with the optimal retention level under four competitive criteria: survival probability, expected profit, variance and expected shortfall of the insurer’s risk. The aggregate claim amounts are assumed to be distributed as compound Poisson, and the individual claim amounts are distributed exponentially. We present an approach to determine the optimal retention level that maximizes the expected profit and the survival probability, whereas minimizing the variance and the expected shortfall of the insurer’s risk. In the decision making process, we concentrate on multi-attribute decision making methods: the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods with their extended versions. We also provide comprehensive analysis for the determination of the optimal retention level under both the expected value and standard deviation premium principles.

Suggested Citation

  • Başak Bulut Karageyik & Şule Şahin, 2017. "Determination of the Optimal Retention Level Based on Different Measures," JRFM, MDPI, vol. 10(1), pages 1-21, January.
    • Handle: RePEc:gam:jjrfmx:v:10:y:2017:i:1:p:4-:d:88747
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/10/1/4/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/10/1/4/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2007. "Extended VIKOR method in comparison with outranking methods," European Journal of Operational Research, Elsevier, vol. 178(2), pages 514-529, April.
    2. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    3. Chi, Yichun & Tan, Ken Seng, 2013. "Optimal reinsurance with general premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 180-189.
    4. Dufresne, François & Gerber, Hans U. & Shiu, Elias S. W., 1991. "Risk Theory with the Gamma Process," ASTIN Bulletin, Cambridge University Press, vol. 21(2), pages 177-192, November.
    5. Cai, Jun & Tan, Ken Seng, 2007. "Optimal Retention for a Stop-loss Reinsurance Under the VaR and CTE Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 93-112, May.
    6. Dickson,David C. M., 2005. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521846400.
    7. Krzysztof Burnecki & Marek Teuerle, 2010. "Ruin Probability in Finite Time," HSC Research Reports HSC/10/04, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    8. Tzeng, Gwo-Hshiung & Lin, Cheng-Wei & Opricovic, Serafim, 2005. "Multi-criteria analysis of alternative-fuel buses for public transportation," Energy Policy, Elsevier, vol. 33(11), pages 1373-1383, July.
    9. Desheng Wu & David L. Olson, 2006. "A TOPSIS Data Mining Demonstration and Application to Credit Scoring," International Journal of Data Warehousing and Mining (IJDWM), IGI Global, vol. 2(3), pages 16-26, July.
    10. Nie, Ciyu & Dickson, David C. M. & Li, Shuanming, 2011. "Minimizing the ruin probability through capital injections," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 195-209, September.
    11. Opricovic, Serafim & Tzeng, Gwo-Hshiung, 2004. "Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS," European Journal of Operational Research, Elsevier, vol. 156(2), pages 445-455, July.
    12. Julien Trufin & Hansjoerg Albrecher & Michel M Denuit, 2011. "Properties of a Risk Measure Derived from Ruin Theory," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 36(2), pages 174-188, December.
    13. Kaishev, Vladimir K. & Dimitrova, Dimitrina S., 2006. "Excess of loss reinsurance under joint survival optimality," Insurance: Mathematics and Economics, Elsevier, vol. 39(3), pages 376-389, December.
    14. Kaluszka, Marek, 2005. "Truncated Stop Loss as Optimal Reinsurance Agreement in One-period Models," ASTIN Bulletin, Cambridge University Press, vol. 35(2), pages 337-349, November.
    15. Bulut Karageyik, Başak & Dickson, David C.M., 2016. "Optimal reinsurance under multiple attribute decision making," Annals of Actuarial Science, Cambridge University Press, vol. 10(1), pages 65-86, March.
    16. Dickson, David C.M. & Waters, Howard R., 1997. "Relative Reinsurance Retention Levels," ASTIN Bulletin, Cambridge University Press, vol. 27(2), pages 207-227, November.
    17. Dickson, David C. M. & Waters, Howard R., 1993. "Gamma Processes and Finite Time Survival Probabilities," ASTIN Bulletin, Cambridge University Press, vol. 23(2), pages 259-272, November.
    18. Dickson, David C.M. & Waters, Howard R., 2006. "Optimal Dynamic Reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 415-432, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shirley Jie Xuan Wang & Kim Leng Poh, 2017. "Intelligent Decision Support in Proportional–Stop-Loss Reinsurance Using Multiple Attribute Decision-Making (MADM)," JRFM, MDPI, vol. 10(4), pages 1-17, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Başak Bulut Karageyik & Şule Şahin, 2016. "Optimal Retention Level for Infinite Time Horizons under MADM," Risks, MDPI, vol. 5(1), pages 1-24, December.
    2. Kaya, Tolga & Kahraman, Cengiz, 2010. "Multicriteria renewable energy planning using an integrated fuzzy VIKOR & AHP methodology: The case of Istanbul," Energy, Elsevier, vol. 35(6), pages 2517-2527.
    3. Wu, Hung-Yi & Lin, Yi-Kuei & Chang, Chi-Hsiang, 2011. "Performance evaluation of extension education centers in universities based on the balanced scorecard," Evaluation and Program Planning, Elsevier, vol. 34(1), pages 37-50, February.
    4. Gwo-Hshiung Tzeng & Chi-Yo Huang, 2012. "Combined DEMATEL technique with hybrid MCDM methods for creating the aspired intelligent global manufacturing & logistics systems," Annals of Operations Research, Springer, vol. 197(1), pages 159-190, August.
    5. Chunguang Bai & Behnam Fahimnia & Joseph Sarkis, 2017. "Sustainable transport fleet appraisal using a hybrid multi-objective decision making approach," Annals of Operations Research, Springer, vol. 250(2), pages 309-340, March.
    6. Ming-Tsang Lu & Gwo-Hshiung Tzeng & Hilary Cheng & Chih-Cheng Hsu, 2015. "Exploring mobile banking services for user behavior in intention adoption: using new hybrid MADM model," Service Business, Springer;Pan-Pacific Business Association, vol. 9(3), pages 541-565, September.
    7. Hisham Alidrisi, 2021. "An Innovative Job Evaluation Approach Using the VIKOR Algorithm," JRFM, MDPI, vol. 14(6), pages 1-19, June.
    8. Serafim Opricovic, 2009. "A Compromise Solution in Water Resources Planning," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(8), pages 1549-1561, June.
    9. Sirirat Sae Lim & Hong Ngoc Nguyen & Chia-Li Lin, 2022. "Exploring the Development Strategies of Science Parks Using the Hybrid MCDM Approach," Sustainability, MDPI, vol. 14(7), pages 1-29, April.
    10. Hsu, C.-H. & Wang, Fu-Kwun & Tzeng, Gwo-Hshiung, 2012. "The best vendor selection for conducting the recycled material based on a hybrid MCDM model combining DANP with VIKOR," Resources, Conservation & Recycling, Elsevier, vol. 66(C), pages 95-111.
    11. Li, Chengjiang & Negnevitsky, Michael & Wang, Xiaolin & Yue, Wen Long & Zou, Xin, 2019. "Multi-criteria analysis of policies for implementing clean energy vehicles in China," Energy Policy, Elsevier, vol. 129(C), pages 826-840.
    12. Jung-Jung Chang & Chia-Li Lin, 2023. "Determining the Sustainable Development Strategies and Adoption Paths for Public Bike-Sharing Service Systems (PBSSSs) under Various Users’ Considerations," Mathematics, MDPI, vol. 11(5), pages 1-30, February.
    13. Najafabadi, Amir T. Payandeh & Bazaz, Ali Panahi, 2018. "An optimal multi-layer reinsurance policy under conditional tail expectation," Annals of Actuarial Science, Cambridge University Press, vol. 12(1), pages 130-146, March.
    14. Dilşad Güzel & Hamit Erdal, 2015. "A Comparative Assesment of Facility Location Problem via fuzzy TOPSIS and fuzzy VIKOR: A Case Study on Security Services," International Journal of Business and Social Research, LAR Center Press, vol. 5(5), pages 49-61, May.
    15. Melis Ercan & Emrah Onder, 2016. "Ranking Insurance Companies in Turkey Based on Their Financial Performance Indicators Using VIKOR Method," International Journal of Academic Research in Accounting, Finance and Management Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Accounting, Finance and Management Sciences, vol. 6(2), pages 104-113, April.
    16. Yousaf Ali & Zain Aslam & Hammad Sajid Dar & UbaidUllah Mumtaz, 2018. "A multi-criteria decision analysis of solid waste treatment options in Pakistan: Lahore City—a case in point," Environment Systems and Decisions, Springer, vol. 38(4), pages 528-543, December.
    17. Song, Zhao-Yu & Lin, Cheng-Wei & Feng, Xuehao & Lee, Paul Tae-Woo, 2024. "An empirical study of the performance of the sixth generation ports model with smart ports with reference to major container ports in mainland China," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    18. Chia-Ling Chang & Chung-Hsin Hsu, 2011. "Applying a Modified VIKOR Method to Classify Land Subdivisions According to Watershed Vulnerability," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(1), pages 301-309, January.
    19. Tsai, Wen-Hsien & Chou, Wen-Chin & Lai, Chien-Wen, 2010. "An effective evaluation model and improvement analysis for national park websites: A case study of Taiwan," Tourism Management, Elsevier, vol. 31(6), pages 936-952.
    20. Chia-Li Lin & Chung-Ling Kuo, 2022. "Establishing Competency Development Evaluation Systems and Talent Cultivation Strategies for the Service Industry Using the Hybrid MCDM Approach," Sustainability, MDPI, vol. 14(19), pages 1-33, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jjrfmx:v:10:y:2017:i:1:p:4-:d:88747. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.