加权均值方差准则下的最优资本分配  

Optimal Capital Allocation Based on Weighted-Mean-Variance Principle

作　　者：李宇宁 张奕[1] 赵军 

机构地区：[1]浙江大学数学科学学院,浙江杭州310027 [2]浙江大学城市学院,浙江杭州310015

出　　处：《应用数学》2018年第1期12-18,共7页Mathematica Applicata

基　　金：浙江省自然科学基金(LY18A010005);教育部人文社会科学研究项目(17YJA910003);国家社科基金重大项目(13&ZD163)

摘　　要：本文考虑相依风险情形下的最优资本分配问题.采用随机加权损失函数,在期望-方差准则下,研究最优资本分配解的存在性,分析加权随机变量选取.进一步,文章提出了以破产概率作为模型评价标准,采用随机模拟的方法分别求解不同模型最优资本分配和相应的破产概率,对模型做出评价.最后,在假设相依风险分别为多元正态分布和多元t分布的情形下,用数值模拟的方法对本文提出的加权期望-方差模型与Dhaene提出的加权均值模型和XU和MAO提出的尾部均值方差模型进行比较,结果显示在破产概率准则下,本文提出的加权期望-方差模型所给出的资金分配比例显著优于其他模型.This paper investigates the optimal capital allocation problem for dependent risks. The weightedmean-variance model is used to study the existence of the optimal capital allocation and analyzeits performances. Furthermore, we propose the ruin probability as the evaluation criteria to investigate the performances of the corresponding optimal capital solutions from differentmodelsby means ofstochastic simulation. Finally, under the assumption that the dependent risks follow multivariate normal distribution or multivariate tdistribution, the weighted-mean-variance modelis compared with the weightedmean model proposed by Dhaene and the weightedtail mean-variance model proposed by XU and MAO through simulation. The numerical results show that from the aspect of ruin probability, the weightedmean-variance modelin this paper has a better performance.

关 键 词：资本分配 期望-方差模型 凸规划 破产概率 

分 类 号：O211[理学—概率论与数理统计] O224[理学—数学]