Author(s)

Yuxia Huang, Chuancun Yin

School of Statistics, Qufu Normal University, Qufu, China.

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.

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

Huang, Y. and Yin, C. (2019) Optimal Reciprocal Reinsurance under GlueVaR Distortion Risk Measures. Journal of Mathematical Finance, 9, 11-24. doi: 10.4236/jmf.2019.91002.