Asymptotic Capital Allocation Based on the Higher Moment Risk Measure for Light-Tailed or Moderately Heavy-Tailed Risks

Under the current prudential regulatory frameworks, such as Solvency II, risk capital allocation has emerged in recent years as a critical risk management mechanism for insurers that operate several lines of business. In this article, we focus on risk capital allocation based on the higher moment (HM) risk measure and link it to a confidence level q∈(0,1). More specifically, we investigate the tail behavior of the Euler capital allocation as q↑1 in the framework where real-valued risks belong to the maximum domain of attraction of the Gumbel distribution. With different settings of the strength of dependence among risks, explicit asymptotic formulas are derived for the aforementioned risk capital allocation. Numerical studies are conducted to examine the performance of these asymptotic formulas in specific scenarios. As further extensions of our findings, we propose a method to determine an approximate reference confidence level that asymptotically equates the HM risk measure to the expected shortfall, and we introduce an extrapolated estimator for the risk capital allocation supported by a simulation study.