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Catastrophe Bond Diversification Strategy Using Probabilistic–Possibilistic Bijective Transformation and Credibility Measures in Fuzzy Environment

Author

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  • Wulan Anggraeni

    (Doctoral Program of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sudradjat Supian

    (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Sukono

    (Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, Sumedang 45363, Indonesia)

  • Nurfadhlina Abdul Halim

    (Faculty of Science and Technology, Universiti Sains Islam Malaysia, Bandar Baru Nilai 71800, Negeri Sembilan, Malaysia)

Abstract

The variety of catastrophe bond issuances can be used for portfolio diversification. However, the structure of catastrophe bonds differs from traditional bonds in that the face value and coupons depend on triggering events. This study aims to build a diversification strategy model framework using probabilistic–possibilistic bijective transformation (PPBT) and credibility measures in fuzzy environments based on the payoff function. The stages of modeling include identifying the trigger distribution; determining the membership degrees for the face value and coupons using PPBT; calculating the average face value and coupons using the fuzzy quantification theory; formulating the fuzzy variables for the yield; defining the function of triangular fuzzy membership for the yield; defining the credibility distribution for the triangular fuzzy variables for the yield; determining the expectation and total variance for the yield; developing a model of the catastrophe bond diversification strategy; the numerical simulation of the catastrophe bond strategy model; and formulating a solution to the simulation model of the diversification strategy using the sequential method, quadratic programming, transformation, and linearization techniques. The simulation results show that the proposed model can overcome the self-duality characteristic not possessed by the possibilistic measures in the fuzzy variables. The results obtained are expected to contribute to describing the yield uncertainty of investing in catastrophe bond assets so that investors can make wise decisions.

Suggested Citation

  • Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Abdul Halim, 2023. "Catastrophe Bond Diversification Strategy Using Probabilistic–Possibilistic Bijective Transformation and Credibility Measures in Fuzzy Environment," Mathematics, MDPI, vol. 11(16), pages 1-30, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3513-:d:1217183
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    References listed on IDEAS

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    1. Jian Liu & Jihong Xiao & Lizhao Yan & Fenghua Wen, 2014. "Valuing Catastrophe Bonds Involving Credit Risks," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-6, April.
    2. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    3. Sergio Ortobelli & Sebastiano Vitali & Marco Cassader & Tomáš Tichý, 2018. "Portfolio selection strategy for fixed income markets with immunization on average," Annals of Operations Research, Springer, vol. 260(1), pages 395-415, January.
    4. Caldeira, João F. & Moura, Guilherme V. & Santos, André A.P., 2016. "Bond portfolio optimization using dynamic factor models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 128-158.
    5. Riza Andrian Ibrahim & Sukono & Herlina Napitupulu, 2022. "Multiple-Trigger Catastrophe Bond Pricing Model and Its Simulation Using Numerical Methods," Mathematics, MDPI, vol. 10(9), pages 1-17, April.
    6. Baltussen, Guido & Post, Gerrit T., 2011. "Irrational Diversification: An Examination of Individual Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(5), pages 1463-1491, October.
    7. Zhang, Wei-Guo & Liu, Yong-Jun & Xu, Wei-Jun, 2012. "A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs," European Journal of Operational Research, Elsevier, vol. 222(2), pages 341-349.
    8. Drobetz, Wolfgang & Schröder, Henning & Tegtmeier, Lars, 2020. "The role of catastrophe bonds in an international multi-asset portfolio: Diversifier, hedge, or safe haven?," Finance Research Letters, Elsevier, vol. 33(C).
    9. Charles C. Yang & Mulong Wang & Xiaoying Chen, 2008. "Catastrophe effects on stock markets and catastrophe risk securitization," Journal of Risk Finance, Emerald Group Publishing, vol. 9(3), pages 232-243, May.
    10. Clara Calvo & Carlos Ivorra & Vicente Liern, 2016. "Fuzzy Portfolio Selection Including Cardinality Constraints and Integer Conditions," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 343-355, July.
    11. Adlane Haffar & Éric Le Fur, 2022. "Dependence structure of CAT bonds and portfolio diversification: a copula-GARCH approach," Journal of Asset Management, Palgrave Macmillan, vol. 23(4), pages 297-309, July.
    12. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    13. Zimbidis, Alexandros A. & Frangos, Nickolaos E. & Pantelous, Athanasios A., 2007. "Modeling Earthquake Risk via Extreme Value Theory and Pricing the Respective Catastrophe Bonds," ASTIN Bulletin, Cambridge University Press, vol. 37(1), pages 163-183, May.
    14. Tang, Qihe & Yuan, Zhongyi, 2019. "Cat Bond Pricing Under A Product Probability Measure With Pot Risk Characterization," ASTIN Bulletin, Cambridge University Press, vol. 49(2), pages 457-490, May.
    15. Charles C. Yang & Mulong Wang & Xiaoying Chen, 2008. "Catastrophe effects on stock markets and catastrophe risk securitization," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 9(3), pages 232-243, May.
    16. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Abdul Halim, 2023. "Single Earthquake Bond Pricing Framework with Double Trigger Parameters Based on Multi Regional Seismic Information," Mathematics, MDPI, vol. 11(3), pages 1-44, January.
    17. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Binti Abdul Halim, 2022. "Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    18. Sukono & Hafizan Juahir & Riza Andrian Ibrahim & Moch Panji Agung Saputra & Yuyun Hidayat & Igif Gimin Prihanto, 2022. "Application of Compound Poisson Process in Pricing Catastrophe Bonds: A Systematic Literature Review," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    19. Li, Ting & Zhang, Weiguo & Xu, Weijun, 2013. "Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investment," Economic Modelling, Elsevier, vol. 31(C), pages 12-17.
    20. Wen Chao & Huiwen Zou, 2018. "Multiple-Event Catastrophe Bond Pricing Based on CIR-Copula-POT Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, June.
    21. Wen Chao & Polinpapilinho Katina, 2021. "Valuing Multirisk Catastrophe Reinsurance Based on the Cox–Ingersoll–Ross (CIR) Model," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-8, February.
    22. Li, Xiang & Qin, Zhongfeng & Kar, Samarjit, 2010. "Mean-variance-skewness model for portfolio selection with fuzzy returns," European Journal of Operational Research, Elsevier, vol. 202(1), pages 239-247, April.
    23. Peter Carayannopoulos & M Fabricio Perez, 2015. "Diversification through Catastrophe Bonds: Lessons from the Subprime Financial Crisis," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(1), pages 1-28, January.
    24. J. David Cummins, 2008. "CAT Bonds and Other Risk‐Linked Securities: State of the Market and Recent Developments," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 11(1), pages 23-47, March.
    25. Clara Calvo & Carlos Ivorra & Vicente Liern, 2012. "On the Computation of the Efficient Frontier of the Portfolio Selection Problem," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-25, October.
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