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本文运用非参数核估计方法对资产组合的在险价值(Value at Risk,VaR)进行估计,得到VaR的非参数核估计公式,并基于VaR的非参数核估计公式建立投资组合选择模型。理论上该模型的目标函数具有良好的光滑性,便于优化问题求解。Monte Carlo模拟结果表明该模型具有大样本性质,估计误差会随着样本容量的增大而下降,且该模型在非对称和厚尾分布下的表现优于当前文献中常用的经验分布法和Cornish-Fisher展开法。基于我国上证50指数及其成份股实际数据的实证结果说明该模型是有效的。
This paper estimates the VaR of VaR by using non-parametric kernel estimation method, obtains the non-parametric kernel estimation formula of VaR, and establishes the portfolio selection model based on VaR non-parametric kernel estimation formula. In theory, the objective function of this model has a good smoothness, which is convenient for solving optimization problems. The results of Monte Carlo simulation show that the model has the properties of large sample, the estimation error will decrease with the increase of sample size, and the performance of the model under asymmetric and thick tail distribution is better than the commonly used empirical distribution method and Cornish -Fisher expansion method. The empirical results based on the empirical data of the SSE 50 Index and its constituent stocks show that the model is effective.