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.