Acta Scientiarum Naturalium Universitatis Pekinensis

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Relative Value-at-Risk: A New Kind of Coherent Risk Measure

HU Dekun, DONG Gang, XU Jicheng   

  1. School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:2005-10-18 Online:2006-09-20 Published:2006-09-20



  1. 北京大学数学科学学院,北京,100871

Abstract: A new coherent risk measure called Relative Value-at-risk(RVaR) was proposed. As a intuitional and meaningful index in insurance and risk control, RVaR has many good properties and is consistent with several often used orders. We offer a criterion to determine the value of parameter ρ and RVaR. Based on the criterion, RVaR is identical with VaR for the normal-distributed risk, bigger than VaR for the fat-tail risk and smaller than VaR for the thin-tail risk. We also prove the representation formula of RVaR and illuminate its purport. Finally, RVaR is applied in risk exchange model and capital allocation model.

Key words: RVaR, VaR, coherent risk, capital allocation, risk exchange

摘要: 提出了一种新的风险度量指标——相对风险价值(RVaR)。它在风险控制、保险、最佳估计等方面都有明确的直观意义,并且满足一致性、风险回避性以及与多种常见序相容的合理性要求,较好地弥补了风险价值的理论缺陷。本文提出的确定RVaR的准则,保证在正态条件下所确定的RVaR与VaR相同。此外还给出并证明了RVaR的表示性公式,讨论了RVaR在风险交换和资本分配等问题上的应用。

关键词: 相对风险价值, 风险价值, 一致风险度量, 资本分配, 风险交换

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