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https://doi.org/10.1007/s11401-012-0723-2

has been cited by the following article:

• TITLE: Optimal Reciprocal Reinsurance under GlueVaR Distortion Risk Measures

  AUTHORS: Yuxia Huang, Chuancun Yin

  KEYWORDS: Distortion Risk Measure, VaR, TVaR, GlueVaR, Marginal Indemnification Function (MIF), Optimal Reciprocal Reinsurance

  JOURNAL NAME: Journal of Mathematical Finance, Vol.9 No.1, January 17, 2019

  ABSTRACT: This article investigates the optimal reciprocal reinsurance strategies when the risk is measured by a general risk measure, namely the GlueVaR distortion risk measures, which can be expressed as a linear combination of two tail value at risk (TVaR) and one value at risk (VaR) risk measures. When we consider the reciprocal reinsurance, the linear combination of three risk measures can be difficult to deal with. In order to overcome difficulties, we give a new form of the GlueVaR distortion risk measures. This paper not only derives the necessary and sufficient condition that guarantees the optimality of marginal indemnification functions (MIF), but also obtains explicit solutions of the optimal reinsurance design. This method is easy to understand and can be simplified calculation. To further illustrate the applicability of our results, we give a numerical example.