Application Of Random Matrix Theory In Finance

The arrival of the era of big data has put forward high requirements on the scope and field of application of our data analysis,especially when the number of variables N i s close to the number of samples T,the application of classical statistical theory has encountered great challenges.This paper mainly takes the investment portfolio problem in the financial field as the starting point,makes a summary of the progress of applying random matrix theory to the large dimension limit,and expounds the method of solving this problem in the form of a book report.We will first introduce the basic related conclusions of random matrices,including the most important Wishart conditional probability distribution,and the Stieltjes transform.Then,by assuming that the true correlation matrix C satisfies certain preconditions such as conjugation,the spectrum and eigenvectors of the sample covariance matrix E are taken as the research objects to find connections between them,and then combine the above results and Bayesian statistical methods to establish the optimal rotationally invariant estimator(RIE)in large-dimensional limit problems.Finally,we will introduce Markowitz portfolio problem in detail,and apply the oracle estimator to the minimum variance risk model,analyze and compare different estimators,and the differences caused by different methods.