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Discrete Time Ruin Probability for Takaful (Islamic Insurance) with Investment and Qard-Hasan (Benevolent Loan) Activities

Author

Listed:
  • Dila Puspita

    (Dept. Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
    Industrial and Financial Mathematics Research Group, Bandung Institute of Technology, Bandung 40132, Indonesia)

  • Adam Kolkiewicz

    (Dept. Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada)

  • Ken Seng Tan

    (Dept. Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
    Current address: Division of Banking and Finance & Insurance Risk and Finance Research Centre, Nanyang Technological University, Singapore 637551, Singapore.)

Abstract

The main objectives of this paper are to construct a new risk model for modelling the Hybrid-Takaful (Islamic Insurance) and to develop a computational procedure for calculating the associated ruin probability. Ruin probability is an important study in actuarial science to measure the level of solvency adequacy of an insurance product. The Hybrid-Takaful business model applies a Wakalah (agent based) contract for underwriting activities and Mudharabah (profit sharing) contract for investment activities. We consider the existence of qard-hasan facility provided by the operator (shareholder) as a benevolent loan for the participants’ fund in case of a deficit. This facility is a no-interest loan that will be repaid if the business generates profit in the future. For better investment management, we propose a separate investment account of the participants’ fund. We implement several numerical examples to analyze the impact of some key variables on the Takaful business model. We also find that our proposed Takaful model has a better performance than the conventional counterpart in terms of the probability of ruin.

Suggested Citation

  • Dila Puspita & Adam Kolkiewicz & Ken Seng Tan, 2020. "Discrete Time Ruin Probability for Takaful (Islamic Insurance) with Investment and Qard-Hasan (Benevolent Loan) Activities," JRFM, MDPI, vol. 13(9), pages 1-24, September.
    • Handle: RePEc:gam:jjrfmx:v:13:y:2020:i:9:p:211-:d:413854
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    References listed on IDEAS

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    1. Costabile, Massimo & Massabó, Ivar & Russo, Emilio, 2008. "A binomial model for valuing equity-linked policies embedding surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 873-886, June.
    2. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook0501, December.
    3. Hayat Khan, 2019. "A Nontechnical Guide on Optimal Incentives for Islamic Insurance Operators," JRFM, MDPI, vol. 12(3), pages 1-14, July.
    4. Stéphane Loisel & Hans-U. Gerber, 2012. "Why ruin theory should be of interest for insurance practitioners and risk managers nowadays," Post-Print hal-00746231, HAL.
    5. Cossette, Helene & Landriault, David & Marceau, Etienne, 2006. "Ruin probabilities in the discrete time renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 309-323, April.
    6. Sung Soo Kim & Steve Drekic, 2016. "Ruin Analysis of a Discrete-Time Dependent Sparre Andersen Model with External Financial Activities and Randomized Dividends," Risks, MDPI, vol. 4(1), pages 1-15, February.
    7. Naseem Al Rahahleh & M. Ishaq Bhatti & Faridah Najuna Misman, 2019. "Developments in Risk Management in Islamic Finance: A Review," JRFM, MDPI, vol. 12(1), pages 1-22, February.
    8. Khan, Hayat, 2015. "Optimal incentives for takaful (Islamic insurance) operators," Journal of Economic Behavior & Organization, Elsevier, vol. 109(C), pages 135-144.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    10. Cheung, Eric C.K. & Landriault, David & Willmot, Gordon E. & Woo, Jae-Kyung, 2010. "Structural properties of Gerber-Shiu functions in dependent Sparre Andersen models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 117-126, February.
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    Cited by:

    1. Lukman Hanif Arbi, 2021. "A Contract Theory Approach to Islamic Financial Securities with an Application to Diminishing Mushārakah," JRFM, MDPI, vol. 14(1), pages 1-12, January.

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