我们讨论了一些经济原因，说明为何在未来数十年内，对价格和收益率统计矩的预测在最好情况下也将仅限于其均值和波动率。这限制了利用高斯分布预测价格和收益率概率的准确性。这些限制的经济根源在于，对基于市场的价格和收益率第 n 阶统计矩（n=1,2,..）进行预测，需要描述第 n 阶经济变量，而这些变量由市场交易的价值或交易量的 n 次幂之和决定。由于缺乏描述由市场交易二次幂之和所决定的经济变量演变的现有模型，甚至连价格和收益率波动率的预测都非常不确定。人们可以忽视我们所强调的现有经济障碍，但无法克服或解决这些障碍。价格和收益率概率预测的准确性在很大程度上决定了资产定价模型和投资组合理论的可靠性。对价格和收益率统计矩预测准确性的限制，降低了现代资产定价和投资组合理论的可靠性与真实性。
英文摘要：
We discuss the economic reasons why the predictions of price and return statistical moments in the coming decades, in the best case, will be limited by their averages and volatilities. That limits the accuracy of the forecasts of price and return probabilities by Gaussian distributions. The economic origin of these restrictions lies in the fact that the predictions of the market-based n-th statistical moments of price and return for n=1,2,.., require the description of the economic variables of the n-th order that are determined by sums of the n-th degrees of values or volumes of market trades. The lack of existing models that describe the evolution of the economic variables determined by the sums of the 2nd degrees of market trades results in the fact that even predictions of the volatilities of price and return are very uncertain. One can ignore existing economic barriers that we highlight but cannot overcome or resolve them. The accuracy of predictions of price and return probabilities substantially determines the reliability of asset pricing models and portfolio theories. The restrictions on the accuracy of predictions of price and return statistical moments reduce the reliability and veracity of modern asset pricing and portfolio theories.
European Commission (DG Joint Research Centre)（欧盟委员会（联合研究中心））；Economics and Econometrics Research Institute (EERI)（经济与计量经济学研究所）；Catholic University of Leuven (LICOS)（鲁汶天主教大学）；Slovak University of Agriculture in Nitra (SUA)（尼特拉斯洛伐克农业大学）
Lagrange statistics in systems (markets) with price constraints: Analysis of property, car sales, marriage and job markets by the Boltzmann function and the Pareto distribution
