股票价格波动的量子分析
A Quantum Approach to Stock Price Fluctuations
摘要：
一个简单的量子模型解释了文献[1]中所观察到的个股收益率的Levy-不稳定分布。[1]的文件。收益率的概率密度函数被写为振幅的平方模。对于短的时间间隔，这个幅度是成比例的柯西分布，并满足薛定谔方程与非厄米哈密顿。观察到的幂律尾部的回报波动意味着“衰减率”，$γ(q)$渐近正比于$|q|$，大$|q|$。波数，傅立叶共轭变量的回报，被解释为“市场情绪”的定量测量。在不到几周的时间尺度上，这个量子模型中的收益分布是形状稳定的，并且是可伸缩的。该模型定量地再现了所观察到的累积分布的短期归一化收益率超过7个数量级，没有可调参数。如果$γ(q\sim 0)\propto q^2$满足，则在长时间段内的收益波动最终变为高斯型。的animals $γ(q)=b_T\sqrt{m^2+q^2}$被发现描述的积极的一部分，所观察到的历史概率的归一化收益的时间段T=5分钟和$T\sim 4$年之间超过4个数量级的一个可调参数$s_T=m b_T\propto T$。在这个模型中，股票的夏普比率有一个有限的极限作为投资期限$T\to 0$。对短期投资的影响进行了讨论。
英文摘要：
A simple quantum model explains the Levy-unstable distributions for individual stock returns observed by ref.[1]. The probability density function of the returns is written as the squared modulus of an amplitude. For short time intervals this amplitude is proportional to a Cauchy-distribution and satisfies the Schroedinger equation with a non-hermitian Hamiltonian. The observed power law tails of the return fluctuations imply that the "decay rate", $γ(q)$ asymptotically is proportional to $|q|$, for large $|q|$. The wave number, the Fourier-conjugate variable to the return, is interpreted as a quantitative measure of "market sentiment". On a time scale of less than a few weeks, the distribution of returns in this quantum model is shape stable and scales. The model quantitatively reproduces the observed cumulative distribution for the short-term normalized returns over 7 orders of magnitude without adjustable parameters. The return fluctuations over large time periods ultimately become Gaussian if $γ(q\sim 0)\propto q^2$. The ansatz $γ(q)=b_T\sqrt{m^2+q^2}$ is found to describe the positive part of the observed historic probability of normalized returns for time periods between T=5 min and $T\sim 4$ years over more than 4 orders of magnitude in terms of one adjustable parameter $s_T=m b_T\propto T$. The Sharpe ratio of a stock in this model has a finite limit as the investment horizon $T\to 0$. Implications for short-term investments are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
