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Normalized Exponential Tilting

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  • Shaun Wang

Abstract

This article discusses methods of risk-neutralizing multivariate probability distributions by applying exponential tilting to the joint probability density function with respect to a set of reference risks. To ensure consistent interpretations of the exponential tilting parameters, a normalization procedure is performed on the reference risks via percentile mapping to standard normal variables. The article establishes links between normalized exponential tilting and multivariate probability distortions. It provides efficient methods for computing risk-neutralized multivariate probability distributions, and it gives illustrative examples in pricing contingent claims on multiple risks.

Suggested Citation

  • Shaun Wang, 2007. "Normalized Exponential Tilting," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 89-99.
    • Handle: RePEc:taf:uaajxx:v:11:y:2007:i:3:p:89-99
    DOI: 10.1080/10920277.2007.10597468
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    Cited by:

    1. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted risk capital allocations," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 263-269, October.
    2. Urbina, Jilber & Guillén, Montserrat, 2013. "An application of capital allocation principles to operational risk," Working Papers 2072/222201, Universitat Rovira i Virgili, Department of Economics.
    3. Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
    4. Boyer, M. Martin & Stentoft, Lars, 2013. "If we can simulate it, we can insure it: An application to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 35-45.
    5. Li, Han & Liu, Haibo & Tang, Qihe & Yuan, Zhongyi, 2023. "Pricing extreme mortality risk in the wake of the COVID-19 pandemic," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 84-106.
    6. Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751, September.
    7. Labuschagne, Coenraad C.A. & Offwood, Theresa M., 2010. "A note on the connection between the Esscher-Girsanov transform and the Wang transform," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 385-390, December.
    8. Qiurong Cui & Zhengjun Zhang, 2018. "Max-Linear Competing Factor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 62-74, January.
    9. Haruyoshi Ito & Jing Ai & Akihiko Ozawa, 2016. "Managing Weather Risks: The Case of J. League Soccer Teams in Japan," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 877-912, December.
    10. Rui Zhou & Guangyu Xing & Min Ji, 2019. "Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM," Risks, MDPI, vol. 7(1), pages 1-18, February.
    11. Kamil J. Mizgier & Joseph M. Pasia & Srinivas Talluri, 2017. "Multiobjective capital allocation for supplier development under risk," International Journal of Production Research, Taylor & Francis Journals, vol. 55(18), pages 5243-5258, September.
    12. Yijia Lin & Sheen Liu & Jifeng Yu, 2013. "Pricing Mortality Securities With Correlated Mortality Indexes," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 921-948, December.
    13. Frédéric Godin & Van Son Lai & Denis-Alexandre Trottier, 2019. "A General Class of Distortion Operators for Pricing Contingent Claims with Applications to CAT Bonds," Working Papers 2019-004, Department of Research, Ipag Business School.

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