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A New Financial Risk Management Model
Duan Yuezhong Economics and Management School of Beijing University of Posts and Telecommunications Duanyuezhong@ta139.com Xie xiguo Economics and Management School of Beijing University of Posts and Telecommunications Xiexiguo@ta139.com Jin Yongsheng Economics and Management School of Beijing University of Posts and Telecommunications jys1900@yahoo.com.cn Cheng Che China University of Petroleum (HD) College of Economics and Management Dongying , China bybsh@hotmail.com
Abstract
To the problem of the financial risk management, the paper brings forward a new model based on main component analysis method and multi-classes support vector machines. In one hand, the main component analysis method was used to reduce the number of indexes and to improve the efficiency. In the other hand, the multi-classes support vector machines was used to classify the warning accurately. Because the new model can not only improve the efficiency but also improve the precision, it is proved that the new model is a more feasible method than any other methods before.
Keyword:
financial risk management, main component analysis method, multi-classes SVM
I. INTRODUCTION
From 1938 to now, there are many models have been used to study financial risk management. For example, RAROC, VaR, Risk Metrics, Credit Metrics, Enterprise total risk management and so on. But these models all have some limitations, like complexity of calculation and low precision [1]. This paper brings forward a new model based on main component analysis method and multi-classes support vector machines. To the problem that there are many indexes to affect financial risk management, the main component analysis method is used to reduce the number of indexes and play down the complexity of analysis. Multi-classes Support vector machine is an important area of statistical learning theory. Because it is based on the structure risk minimize and can disposal the small swatch, it holds the better extensive ability [4]. It is the abreast of the times and the most accurate method. Therefore, the new model based on main component analysis method and multi-classes support vector machines can not only improve the efficiency but also improve the precision, it is proved that the new model is a more feasible method than any other methods before. The paper includes 4 sections. Section 2 introduces theories related to rough set and multi-classes support vector machine. Section 3 elaborates on the model proposed in this study. Section 4 concludes the study.
II.Theories related to rough set and multi-classes SVM
This section will introduce the theories related to main component analysis method and multi-classes support vector machine.
A. Main component analysis method
Main component analysis method is a multivariate statistical analysis method, which changes several indexes into few comprehensive ones. It adopts a method to reduce indexes and find out some comprehensive variables to represent the srcinal ones. The unrelated comprehensive ones can possibly reflect
2009 Third International Symposium on Intelligent Information Technology Application
978-0-7695-3859-4/09 $26.00 © 2009 IEEEDOI 10.1109/IITA.2009.140194
2009 Third International Symposium on Intelligent Information Technology Application
978-0-7695-3859-4/09 $26.00 © 2009 IEEEDOI 10.1109/IITA.2009.140194
the srcinal information. The basic steps of multivariable comprehensive evaluation by using main component analysis method are as follows[6]: 1
．
Indexes’ standardization the number of sample is n
，
the number of index is m
X
＝（
X
ij
）
n
×
m
i
＝
1
，
2
，
.....n. j
＝
1
，
2
，
..... m, X
ij
represents the variable of index j of sample i . The formula is Y
ij
＝
( X
ij
－
X
j
) / S
j
X
j
＝
n
1
=
ni
1
X
ij
S
j
＝
[
11
−
n
∑
=
ni
1
( X
ij
－
X
j
)
2
]
1/2
2
．
Calculation of the covariance matrix R
R
＝
[r
ij
]
m
×
m
r
ij
is the correlation coefficient of
X
i
and X
j
.
3
．
Calculation of the eigenvalues and the eigenvectors of the covariance matrix R. We use the eigenequation to get eigenvalues in numerical order and relevant eigenvectors.
Because of
0][
=−
R I
λ
We get eigenvalues
λ
1
、λ
2
、λ
3………
λ
m in numerical order and relevant eigenvectors U1
、
U2
、
U3
、
………Um
U
i
＝（
u
i1
，
u
i2
，
u
i3
.......... u
im
）。
Then the main component
Z
i
＝
u
i1
Y
i1
＋
u
i2
Y
i2
＋
……….
＋
u
im
Y
im
i
＝
1
、
2
、
3……..m 4.
The process of the l main component analysis method is as follows: The weight of each main component is
Q
i
＝λ
i
/
∑
=
mi
1
λ
i
. According to
∑
=
wi
1
λ
i
/
∑
=
mi
1
λ
i
>85%,
We select the first
w main components to conduct calculation.
. F
＝
∑
=
w f
1
Ff
＝
∑
=
w f
1
Q
f
×
Z
f
，
f
＝
1
、
2
、
3……..w
Finally, we can compare each F and then place them in numerical order. These are the theories related to the main component analysis method.
B. Multi-classes SVM
The support vector machine is a new and promising classification and regression technique proposed by Vapnik and his group at AT&T Bell Laboratories. The SVM learns a separating hyperplane to maximize the margin and to produce a goad generalization capability. Recent theoretical research work has solved existing difficulties in using the SVM in practical applications. Until now, it has been successfully applied in many areas, such as face detection, hand-written digit recognition, and data mining, etc[8]. In theory, SVM classification can be traced back to the classical structural risk minimization (SRM) approach, which determines the classification decision function by minimizing the empirical risk, as
R
=
k
1
∑
=
−
k i
y x f
1
)(
where
k
a
nd f represent the size of examples and the classification decision function, respectively. For SVM, the primary concern is determining an optimal separating hyperplane that gives a tow generalization error. Usually, the classification decision function in the linearly separable problem is represented by[12]
f(x)
=
sign
(w
x
+
b
)
In SVM, the optimal separating hyperplane is determined by giving the largest margin of separation between different classes. This optimal hyperplane bisects the shortest line between the convex hulls of the two classes. The optimal hyperplane is required to satisfy the following constrained minimization, as
195
195
Min
:
21
w
2
y
i
(
w
x
i
+
b
)
≥
1
For the linearly non-separable case, the minimization problem can be modified to allow misclassified data points. SVM can he applied to mufti-class classification by combining SVMs[12].
Min
φ
(
w
,
ζ
)
=
21
w
2
+
C
∑
=
l i
1
∑
≠
ym
ζ
mi
s.t.
(
w
yi
x
i
)
＋
b
yi
≥
(
w
m
x
i
)
＋
b
m
＋
2
—
ζ
mi
ζ
mi
≥
0 i = 1,2 .......
l m, y
i
∈
{1,2,........,k}
m
≠
y
i
The decision function is as follow
f(x)
=
argmax
[(
w
i
x
)
＋
b
i
], i = 1,2 .......
k.
These are the theories related to the multi-classes support vector machine.
III.The introduction of the new model
The paper divided the level of financial risk into five grades: low, lower, middle, higher, high. Then we use twelve indexes to value the financial risk: diversification, liquidity, asset/ liability, valuation of assets, trading control, transparency, economic intelligence, capital adequacy, asset quality, financial information, intellectual property of financial product, financial intelligence system. First, we used the main component analysis method to delete some indexes which are not important to the information system security value. Second, the data set is divided into 5 parts. Each data set is input to their opposite SVM. The scores of different classes are added up and the class which has the highest score is accepted as the class of the warning system. Third, the data set is divided into two parts: some are training data, the other are testing data. The training data are trained by SVRM, and the testing data are input to the SVRM which has been trained to test the SVRM. At last, the new data may be input into the model and we may get the five grades of the financial risk’ level. The chart of the model based on fuzzy theory and multi-classes support vector machine is as follow.
Figure1. The chart of the new model
IV. Conclusions
Main component analysis method
Multi
classes support vector machine
The srcin training data
The main component analysis method
The second training data
Testing data
SVM1 SVM2 SVM5
196
196
The paper brings forward a new model based on main component analysis method and multi-classes support vector machines. To the problem that there are many indexes to affect financial risk management, the main component analysis method is used to reduce the number of indexes and play down the complexity of analysis. Multi-classes Support vector machine is an important area of statistical learning theory. Because it is based on the structure risk minimize and can disposal the small swatch, it holds the better extensive ability[4]. It is the abreast of the times and the most accurate method. Therefore, the new model based on main component analysis method and multi-classes support vector machines can not only improve the efficiency but also improve the precision, it is proved that the new model is a more feasible method than any other methods before.
Reference
[1] HUANG Hai-feng, MA Hong-yi, the main methods of Chinese financial risk management, Economic Theories and Economic Management, 2005. [2] ZHANG Xi-yu, the VAR method of financial risk management, Enterprise Economy, January 2003. [3] GU Xiu-juan, the financial risk management: the development of theories and technologies, Economic Survey, No 1, 2007. [4] XIAO Wenbind, FEI Qi, a Study of Personal Credit Scoring Models on Support Vector Machine with Optimal Choice of Kernel Function Parameters, Systems Engineering Theory & Practice, the tenth, 2006 [5] TANG Jia-fu, LI Run-sheng, SHI Yong-gui, FAN Chun-guang, Application of Principal Component Analysis to Performance Evaluation of Telecom Enterprises,
Journal of Northeastern University (Natural Science), No 4, 2008. [6]
Jiang Huiyuan, Wang Wanxiang, Application of Principal Component Analysis in Synthetic Appraisal for Multi-objects Decision-making, Journal of Wuhan University of Technology
,
No 4, 2003. [7] XIA Guoen, JING Weidong, ZHANG Gexiang, Synthetic Evaluation Method Baste Support Vector Classifier and Regression Machine, Journal of Southwest Jiaotong University, Vol 41, 2006. [8] XIAO Wenbind, FEI Qi, a Study of Personal Credit Scoring Models on Support Vector Machine with Optimal Choice of Kernel Function Parameters, Systems Engineering Theory & Practice, the tenth, 2006. [9] Steve Gunn, Support Vector Machines for Classification and Regression , Image Speech and Intelligent Systems Group, 10 May 1998. [10] Harris Drucker, Chris J.C. Burges, Linda Kaufman, Alex Smola, Vladimir Vapnik, Support Vector Regression Machines, Advances in Neural Information Processing Systems, 1997: 9(S): 155-161. [11] Dacheng Tao, Xiaoou Tang, Xuelong Li, and Xindong Wu, Asymmetric Bagging and Random Subspace for Support Vector Machines-Based Relevance Feedback in Image Retrieval, IEEE Transactions on Pattern Analysis and Machine Intelligence, VOL. 28, NO.7, 2006, pp.1088-1099. [12] GAO Shang, YANG Jingyu, Assessing the effectiveness based on principal component analysis and support vector machine, Systems Engineering and Electronics, Vo1.28, No.6, 2006.
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