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Computing best bounds for nonlinear risk measures with partial information

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  • Wong, Man Hong
  • Zhang, Shuzhong

Abstract

Extreme events occur rarely, but these are often the circumstances where an insurance coverage is demanded. Given the first, say, n moments of the risk(s) of the events, one is able to compute or approximate the tight bounds for risk measures in the form of E(ψ(x)) through semidefinite programmings (SDP), via distributional robust optimization formulations. Existing results in the literature have already demonstrated the power of this technique when ψ(x) is linear or piecewise linear. In this paper, we extend the technique in the case where ψ(x) is a polynomial or fractional polynomial.

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  • Wong, Man Hong & Zhang, Shuzhong, 2013. "Computing best bounds for nonlinear risk measures with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 204-212.
  • Handle: RePEc:eee:insuma:v:52:y:2013:i:2:p:204-212
    DOI: 10.1016/j.insmatheco.2012.12.006
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    3. Hu, Xiang & Duan, Baige & Zhang, Lianzeng, 2017. "De Vylder approximation to the optimal retention for a combination of quota-share and excess of loss reinsurance with partial information," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 48-55.
    4. Hu, Xiang & Yang, Hailiang & Zhang, Lianzeng, 2015. "Optimal retention for a stop-loss reinsurance with incomplete information," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 15-21.
    5. András Prékopa & Anh Ninh & Gabriela Alexe, 2016. "On the relationship between the discrete and continuous bounding moment problems and their numerical solutions," Annals of Operations Research, Springer, vol. 238(1), pages 521-575, March.

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