改进的Atlas模型下市场的稳定分布

Atlas模型在随机投资组合理论中有广泛的应用,但它的假定具有一定的局限性．我们对该模型进行了改进,证明了满足改进的Atlas模型的市场是渐进稳定的;在改进的Atlas模型下我们得到了市场稳定分布的确定性等价近似以及不同投资组合的渐近增长率与渐近超额增长率,这些结果与Atlas模型的类似结果相比有很大的优点;同时我们使用中国股票市场的交易数据对资本的稳定分布以及某些投资组合的长期平均增长率进行了实证研究,对比市场平均资本分布以及Atlas模型的相应结果,我们改进的Atlas模型在实证上比Atlas模型具有更好的适用性．

The Stable Capital Distribution under Improved Atlas Model

An important model in the stochastic portfolio theory is the Atlas model,but its assumptions seem too restrictive.We present an improvement of the Atlas model and prove that the market under this model is asymptotically stable.Within this model,we study the stable capital distribution of the equity market and the asymptotic long-term growth rate of various portfolios,and illustrate that these results are much better than those of the Atlas model.As an empirical study,we estimate the stable distribution and long-term growth rate of various portfolios by using the trading data in China Stock Market.Compared with the theoretical average capital distribution and the Atlas model,our model provides better applicability.