<p style='text-indent:20px;'>Modeling of uncertainty by probability errs by ignoring the uncertainty in probability. When financial valuation recognizes the uncertainty of probability, the best the market may offer is a two price framework of a lower and upper valuation. The martingale theory of asset prices is then replaced by the theory of nonlinear martingales. When dealing with pure jump compensators describing probability, the uncertainty in probability is captured by introducing parametric measure distortions. The two price framework then alters asset pricing theory by requiring two required return equations, one each for the lower upper valuation. Proxying lower and upper valuations by daily lows and highs, the paper delivers the first empirical study of nonlinear martingales via the modeling and simultaneous estimation of the two required return equations.</p>

中文翻译：

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金融资产定价上下限

<p style='text-indent:20px;'>通过忽略概率中的不确定性，通过概率错误建模不确定性。当财务估值认识到概率的不确定性时，市场可能提供的最好的价格是较低估值和较高估值的两个价格框架。资产价格的鞅理论随后被非线性鞅理论所取代。在处理描述概率的纯跳跃补偿器时，通过引入参数测量失真来捕获概率的不确定性。然后，两个价格框架通过要求两个所需回报方程来改变资产定价理论，每个方程用于较低的估值上限。通过每日低点和高点来代表较低和较高的估值，