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Bounding Basis-Risk Using s-convex Orders on Beta-unimodal Distributions

Author

Listed:
  • Claude Lefèvre

    (ULB - Département de Mathématique [Bruxelles] - ULB - Faculté des Sciences [Bruxelles] - ULB - Université libre de Bruxelles)

  • Stéphane Loisel

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Pierre Montesinos

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

This paper is concerned with properties of Beta-unimodal distributions and their use to assess the basis risk inherent to index-based insurance or reinsurance contracts. To this extent, we first characterize s-convex stochastic orders for Beta-unimodal distributions in terms of the Weyl fractional integral. We then determine s-convex extrema for such distributions , focusing in particular on the cases s = 2, 3, 4. Next, we define an Enterprise Risk Management framework that relies on Beta-unimodality to assess these hedge imperfections , introducing several penalty functions and worst case scenarios. Some of the results obtained are illustrated numerically via a representative catastrophe model.
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Suggested Citation

  • Claude Lefèvre & Stéphane Loisel & Pierre Montesinos, 2020. "Bounding Basis-Risk Using s-convex Orders on Beta-unimodal Distributions," Post-Print hal-02611227, HAL.
    • Handle: RePEc:hal:journl:hal-02611227
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    References listed on IDEAS

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    1. Linda L. Golden & Mulong Wang & Chuanhou Yang, 2007. "Handling Weather Related Risks Through the Financial Markets: Considerations of Credit Risk, Basis Risk, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 319-346, June.
    2. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    3. Kazushi Takahashi & Christopher B Barrett & Munenobu Ikegami, 2019. "Does Index Insurance Crowd In or Crowd Out Informal Risk Sharing? Evidence from Rural Ethiopia," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 101(3), pages 672-691.
    4. Jensen, Nathaniel D. & Mude, Andrew G. & Barrett, Christopher B., 2018. "How basis risk and spatiotemporal adverse selection influence demand for index insurance: Evidence from northern Kenya," Food Policy, Elsevier, vol. 74(C), pages 172-198.
    5. Kaas, R & Goovaerts, M, 1985. "Bounds On Distribution Functions Under Integral Constraints," University of Amsterdam, Actuarial Science and Econometrics Archive 293091, University of Amsterdam, Faculty of Economics and Business.
    6. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    7. De Vylder, F. & Goovaerts, M. J., 1982. "Analytical best upper bounds on stop-loss premiums," Insurance: Mathematics and Economics, Elsevier, vol. 1(3), pages 163-175, July.
    8. Hélène Cossette & Thierry Duchesne & Étienne Marceau, 2003. "Modeling Catastrophes and their Impact on Insurance Portfolios," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 1-22.
    9. Enkelejd Hashorva & Lanpeng Ji, 2014. "Random Shifting and Scaling of Insurance Risks," Risks, MDPI, vol. 2(3), pages 1-12, July.
    10. Alexandru V. Asimit & Raluca Vernic & Ricardas Zitikis, 2016. "Background Risk Models and Stepwise Portfolio Construction," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 805-827, September.
    11. J. David Cummins & Mary A. Weiss, 2009. "Convergence of Insurance and Financial Markets: Hybrid and Securitized Risk‐Transfer Solutions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 493-545, September.
    12. De Vylder, F., 1982. "Best upper bounds for integrals with respect to measures allowed to vary under conical and integral constraints," Insurance: Mathematics and Economics, Elsevier, vol. 1(2), pages 109-130, April.
    13. Robert L. Winkler & Gary M. Roodman & Robert R. Britney, 1972. "The Determination of Partial Moments," Management Science, INFORMS, vol. 19(3), pages 290-296, November.
    14. Côté, Marie-Pier & Genest, Christian, 2019. "Dependence in a background risk model," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 28-46.
    15. De Vylder, F., 1983. "Maximization, under equality constraints, of a functional of a probability distribution," Insurance: Mathematics and Economics, Elsevier, vol. 2(1), pages 1-16, January.
    16. Kaas, R. & Goovaerts, M. J., 1986. "Best bounds for positive distributions with fixed moments," Insurance: Mathematics and Economics, Elsevier, vol. 5(1), pages 87-92, January.
    17. Cassandra R. Cole & Kathleen A. McCullough, 2006. "A Reexamination of the Corporate Demand for Reinsurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 169-192, March.
    18. Denuit, Michel, 1999. "The Exponential Premium Calculation Principle Revisited," ASTIN Bulletin, Cambridge University Press, vol. 29(2), pages 215-226, November.
    19. Anne Gron, 1999. "Insurer Demand for Catastrophe Reinsurance," NBER Chapters, in: The Financing of Catastrophe Risk, pages 23-50, National Bureau of Economic Research, Inc.
    20. Hashorva, Enkelejd, 2003. "On the number of near-maximum insurance claim under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 37-49, February.
    21. Chi, Yichun & Yang, Jingping & Qi, Yongcheng, 2009. "Decomposition of a Schur-constant model and its applications," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 398-408, June.
    22. Enkelejd Hashorva & Anthony G. Pakes & Qihe Tang, 2010. "Asymptotics of Random Contractions," Papers 1008.0126, arXiv.org.
    23. Constantinescu, Corina & Hashorva, Enkelejd & Ji, Lanpeng, 2011. "Archimedean copulas in finite and infinite dimensions—with application to ruin problems," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 487-495.
    24. Ghada Elabed & Marc F. Bellemare & Michael R. Carter & Catherine Guirkinger, 2013. "Managing basis risk with multiscale index insurance," Agricultural Economics, International Association of Agricultural Economists, vol. 44(4-5), pages 419-431, July.
    25. Hashorva, Enkelejd & Pakes, Anthony G. & Tang, Qihe, 2010. "Asymptotics of random contractions," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 405-414, December.
    26. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
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