论文标题
脂肪的尾巴是由供需的资产价格内源性出现的，有或没有跳跃过程
Fat tails arise endogenously in asset prices from supply/demand, with or without jump processes
论文作者
论文摘要
我们表明，跳跃扩散类型的征费工艺的商具有脂肪尾分布。应用于经济学的价格理论。我们表明，脂肪尾巴是基于过量需求分析的价格变化而产生的。假设是供需用漂移术语，布朗尼（即高斯）和复合泊松跳动过程描述。如果$ p^{ - 1} dp /dt $（间隔$ dt $中的相对价格变化）由相对多余需求的适当函数给出，则$ \ weft（\ Mathcal {d}％ - \ Mathcal {s} \ right） /\ Mathcal {s} $（wher）分布的尾巴行为$ f \ left（x \ right）\ sim x^{ - ζ} $对于power $ζ$，它取决于$ p^{ - 1} dp/dt = g \ left的函数$ g $ in $ g $，对于$ g \ left（x \ right）\ sim \ left \ vert x \ right \ vert \ vert ^{1/q} $一个一个具有$ζ= q。$，资产的经验数据通常会产生一个值，$ $ζ\ tilde {=} 3，=} 3，$或$ \ $ \中的\ in \ weft [3,3,5,5，5，right] for Soments ins for Soments sosers for Soments ins for Soments。 如果人们使用基本经济学方法（即通用的沃尔拉斯式调整）建模价格动态，而不是普通的古典财务出发点，那是假设价格变化正常的经典融资，那么经验结果与理论之间的差异永远不会产生。功能$ g $是确定性的，可以使用较小的数据集进行校准。结果在密度函数的衰减指数与价格调整功能之间建立了一个简单的联系，该功能可以改善风险评估的方法。 数学结果可以应用于其他问题，涉及跳投类型的相对差异或商的相对差异或商。
We show that the quotient of Levy processes of jump-diffusion type has a fat-tailed distribution. An application is to price theory in economics. We show that fat tails arise endogenously from modeling of price change based on an excess demand analysis resulting in a quotient of arbitrarily correlated demand and supply whether or not jump discontinuities are present. The assumption is that supply and demand are described by drift terms, Brownian (i.e., Gaussian) and compound Poisson jump processes. If $P^{-1}dP/dt$ (the relative price change in an interval $dt$) is given by a suitable function of relative excess demand, $\left( \mathcal{D}% -\mathcal{S}\right) /\mathcal{S}$ (where $\mathcal{D}$ and $\mathcal{S}$ are demand and supply), then the distribution has tail behavior $F\left( x\right) \sim x^{-ζ}$ for a power $ζ$ that depends on the function $G$ in $P^{-1}dP/dt=G\left( \mathcal{D}/\mathcal{S}\right) $. For $G\left( x\right) \sim\left\vert x\right\vert ^{1/q}$ one has $ζ=q.$ The empirical data for assets typically yields a value, $ζ\tilde{=}3,$ or $\ ζ\in\left[ 3,5\right] $ for some markets. The discrepancy between the empirical result and theory never arises if one models price dynamics using basic economics methodology, i.e., generalized Walrasian adjustment, rather than the usual starting point for classical finance which assumes a normal distribution of price changes. The function $G$ is deterministic, and can be calibrated with a smaller data set. The results establish a simple link between the decay exponent of the density function and the price adjustment function, a feature that can improve methodology for risk assessment. The mathematical results can be applied to other problems involving the relative difference or quotient of Levy processes of jump-diffusion type.
