基于Laplace分布和CVaR的投资组合模型研究

Research on Investment Portfolio Model Based on Laplace Distribution and CVaR

金融资产收益率的实际分布具有显著的尖峰肥尾性,Laplace分布比正态分布能更好地刻画尖峰肥尾性;引入Laplace分布,得到了风险价值VaR和条件风险价值CVaR的计算公式;建立了均值-CVaR投资组合模型,得到了模型有效前沿和最优解的表达式;最后采用沪深股市的股票进行实证研究,并与正态分布下的均值-CVaR有效前沿进行了比较,结果表明了模型的有效性和算法的合理性.

The real distribution of financial assets earnings has the obvious characteristics of steep peaks and heavy tails and Laplace distribution can better describe the characteristics than normal distribution. This paper obtains the computation formula of value at risk （VaR） and conditional value at risk （CVaR） by introducing Laplace distribution, sets up mean-CVaR investment portfolio model, receives the formula of the efficient frontier of the model and optimal solution, and finally uses the data of Shanghai Stock Exchange and Shenzhen Stock Exchange to conduct empirical research and to compare it with the efficient frontier of mean-CVaR under normal distribution. The results reveal the validity of the model and the rationality of the algorithm.