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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．
Atlas model has a wide range of applications in stochastic portfolio theory, but its assumptions have some limitations. We have improved the model and proved that the market satisfying the improved Atlas model is asymptotical and stable. Under the improved Atlas model, we obtain the deterministic equivalence approximation of the stable market distribution and the asymptotic growth rate of the different portfolios Asymptotic excess growth rate, these results have great advantages compared with the similar results of the Atlas model; at the same time, we use the transaction data of the Chinese stock market to study the steady distribution of capital and the long-term average growth rate of some investment portfolios , Comparing the average market capital distribution with the corresponding results of the Atlas model, our improved Atlas model is empirically more applicable than the Atlas model.