AAM  >> Vol. 5 No. 3 (August 2016)

    基于RORAC和MSD的多目标最优比例再保险
    Multi-Objective Optimal Proportional Reinsurance Based on RORAC and MSD

  • 全文下载: PDF(951KB) HTML   XML   PP.455-471   DOI: 10.12677/AAM.2016.53057  
  • 下载量: 406  浏览量: 482   国家自然科学基金支持

作者:  

杨潇潇,梁志彬,张彩斌:南京师范大学数学科学学院,江苏 南京

关键词:
多目标规划风险调整资本收益率单位标准差收益条件风险价值Pareto最优Multi-Objective Programming RORAC MSD CVaR Pareto Optimization

摘要:
本文引入金融行业在风险管理和绩效评估等方面所常用的指标——风险调整资本收益率(RORAC),以及单位标准差收益(MSD),在资本约束范围内与条件风险价值(CVaR)建立多目标模型。在期望保费原理下,考虑扩散逼近风险模型中基于RORAC和MSD,以及CVaR的最优比例再保险问题。利用多目标优化理论,我们得到了比例再保险的Pareto最优解。最后,通过数值举例,探讨了初始资本水平,保险年度以及风险喜恶对最优再保险策略的影响。

In this paper, based on some indexes which are always used in risk management and performance appraisals for financial industry, such as return on risk adjusted capital (RORAC) and mean-standard deviation (MSD), we construct two multi-objective optimization models together with conditional value at risk (CVaR) as well as the capital regulation. Under the expected value premium principle, by the multi-objective optimization theory, we obtain the Pareto optimal proportional reinsurance strategy for the diffusion approximation risk model. Some numerical examples are given to show the impact of some important parameters, like initial capital and insurance year as well as risk aversion, on the optimal reinsurance strategy.

文章引用:
杨潇潇, 梁志彬, 张彩斌. 基于RORAC和MSD的多目标最优比例再保险[J]. 应用数学进展, 2016, 5(3): 455-471. http://dx.doi.org/10.12677/AAM.2016.53057

参考文献

[1] Cai, J. and Tan, K.S. (2007) Optimal Retention for a Stop-Loss Reinsurance under the VaR and CTE Risk Measures. ASTIN Bulletin, 37, 93-112.
http://dx.doi.org/10.2143/AST.37.1.2020800
[2] Cai, J., Tan, K.S., Weng, C.G. and Zhang, Y. (2008) Optimal Reinsurance under VaR and CTE Risk Measures. Insurance: Mathematics and Economics, 43, 185-196.
http://dx.doi.org/10.1016/j.insmatheco.2008.05.011
[3] Liang, Z.B. and Guo, J.Y. (2010) Optimal Proportional Reinsurance under Two Criteria: Maximizing the Expected Utility and Minimizing the VaR. ANZIAM, 51, 449-463.
[4] Guerra, M. and de Lourdes Centeno, M. (2008) Optimal Reinsurance Policy: The Adjustment Coefficient and the Expected Utility Criteria. Insurance: Mathematics and Economics, 42, 529-539.
http://dx.doi.org/10.1016/j.insmatheco.2007.02.008
[5] 李秀芳, 景珮. 基于多目标规划的最优再保险策略[J]. 天津大学学报(社会科学版), 2013, 15(1): 5-9.
[6] 周明, 寇炜, 李宏军.基于夏普比率的最优再保险策略[J]. 数理统计与管理, 2013, 32(5): 910-922.
[7] 周明, 陈建成, 董洪斌. 风险调整资本收益率下的最优再保险策略[J]. 系统工程理论与实践, 2010, 30(11): 1931- 1937.
[8] Grandell, J. (1991) Aspects of Risk Theory. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-1-4613-9058-9
[9] Ehrgott, M. (2000) Multicriteria Optimization. Springer-Verlag, Berlin.
http://dx.doi.org/10.1007/978-3-662-22199-0