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Random Shifting and Scaling of Insurance Risks

Listed author(s):
  • Enkelejd Hashorva


    (Department of Actuarial Science, University of Lausanne, Bâtiment Extranef, UNIL-Dorigny, Lausanne 1015, Switzerland)

  • Lanpeng Ji


    (Department of Actuarial Science, University of Lausanne, Bâtiment Extranef, UNIL-Dorigny, Lausanne 1015, Switzerland)

Registered author(s):

    Random shifting typically appears in credibility models whereas random scaling is often encountered in stochastic models for claim sizes reflecting the time-value property of money. In this article we discuss some aspects of random shifting and random scaling of insurance risks focusing in particular on credibility models, dependence structure of claim sizes in collective risk models, and extreme value models for the joint dependence of large losses. We show that specifying certain actuarial models using random shifting or scaling has some advantages for both theoretical treatments and practical applications.

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    Article provided by MDPI, Open Access Journal in its journal Risks.

    Volume (Year): 2 (2014)
    Issue (Month): 3 (July)
    Pages: 1-12

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    Handle: RePEc:gam:jrisks:v:2:y:2014:i:3:p:277-288:d:38449
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    1. Albrecher, Hansjörg & Constantinescu, Corina & Loisel, Stephane, 2011. "Explicit ruin formulas for models with dependence among risks," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 265-270, March.
    2. Kume, Alfred & Hashorva, Enkelejd, 2012. "Calculation of Bayes premium for conditional elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 632-635.
    3. Frees, Edward W. & Valdez, Emiliano A., 2008. "Hierarchical Insurance Claims Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1457-1469.
    4. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, Open Access Journal, vol. 1(1), pages 1-20, March.
    5. Yang, Xipei & Frees, Edward W. & Zhang, Zhengjun, 2011. "A generalized beta copula with applications in modeling multivariate long-tailed data," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 265-284, September.
    6. Hashorva, Enkelejd & Kortschak, Dominik, 2014. "Tail asymptotics of random sum and maximum of log-normal risks," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 167-174.
    7. Yang, Yang & Hashorva, Enkelejd, 2013. "Extremes and products of multivariate AC-product risks," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 312-319.
    8. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    9. 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.
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