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# Evolution of distributions of key agregate variables of Russian banks

Student: Dmitrij Malakhov

Supervisor:

Faculty: Faculty of Economic Sciences

Educational Programme: Master

Year of Graduation: 2014

<p align="left" class="aCxSpFirst" style="margin-bottom: 0.0001pt;"><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">In this work we propose a model of evolution of distribution of key aggregate variables of Russian banks. We choose aggregate assets as main analyzed variables, because it is good approximation of banks size. This model &nbsp;is based on basic model of money distribution among banks. Solution of this model describes the dynamic of distribution of banks&rsquo; shares (and this distribution is stable).<o:p></o:p></span></p><p align="left" class="aCxSpMiddle" style="margin-bottom: 0.0001pt;"><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">We test our model: lognormal distribution is good approximation for stable distribution, but average value and standard deviation are not stationary processes. So</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">model</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">passed</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">partially</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">an</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">empirical</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"> </span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">test</span><span style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">.</span><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;"><o:p></o:p></span></p><p align="left" class="aCxSpLast" style="margin-bottom: 0.0001pt;"><span lang="EN-US" style="font-size: 10pt; line-height: 150%; font-family: 'Times New Roman', serif;">Also lognormal distribution is good approximation of distributions of other key variables. &nbsp;In this paper we test so called Gibrat law and we found out, that this law holds for our data. As well this model could be helpful for forecast of dynamic of bank system.&nbsp;<o:p></o:p></span></p>

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