Abstract
A stochastic analysis of financial data is presented. In particular we investigate how the statistics of log returns change with different time delays t. The scale-dependent behaviour of financial data can be divided into two regions. The first time range, the small-timescale region (in the range of seconds) seems to be characterised by universal features. The second time range, the medium-timescale range from several minutes upwards can be characterised by a cascade process, which is given by a stochastic Markov process in the scale τ. A corresponding Fokker–Planck equation can be extracted from given data and provides a non-equilibrium thermodynamical description of the complexity of financial data.

Keywords: Banks; Financial markets; Stochastic processes; Fokker–Planck equation

摘要
財務(wù)數(shù)據(jù)隨機分析已經(jīng)被提出，特別是我們探討如何統(tǒng)計在不同時間τ記錄返回的變化。財務(wù)數(shù)據(jù)的時間規(guī)模依賴行為可分為兩個區(qū)域：第一個時間范圍是被描述為普遍特征的小時間區(qū)域（范圍秒）。第二個時間范圍是增加了幾分鐘的可以被描述為隨機馬爾可夫規(guī)模的級聯(lián)過程的中期時間范圍。相應(yīng)的Fokker - Planck方程可以從特定的數(shù)據(jù)提取，并提供了一個非平衡熱力學描述的復(fù)雜的財務(wù)數(shù)據(jù)。

關(guān)鍵詞：銀行；金融市場；隨機過程；Fokker - Planck方程
1 導(dǎo)言
銀行的財務(wù)報表分析不同于制造業(yè)和服務(wù)業(yè)的公司。因此，一家銀行的財務(wù)報表分析，需要用一個獨特的方法來認識一家銀行有哪些獨特的風險
銀行需要對儲戶的存款帳戶支付部分利息。他們通過對這些基金