Innovative Computing on Finance, ICICIC2007
Conference session C17
A Novel Prediction Model for
Credit Card Risk Management
Tsung

Nan Chou
Department of Finance, Chaoyang University of Technology
168 Jifong E. Rd., Wufong Township, Taichung County, 41349, Taiwan
E

mail: tnchou@mail.cyut.edu.tw
Innovative Computing on Finance, ICICIC2007
Conference session C17
Outline
1.
Introduction
2.
Integrated Model
3.
Research Methodologies
–
Evolutional neural network
–
Grey incidence analysis
–
Dempster

Shafer theory
4.
Experiment Results
5.
Conclusion
Innovative Computing on Finance, ICICIC2007
Conference session C17
Introduction
Credit Card Business in Taiwan
•
The severe competition of credit card
market in Taiwan.
•
The amount of issued credit cards has
increased rapidly and is sixteen times the
size of the past decade issues
•
The annual amount of credit has also
growth 9.54 times.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Introduction
The Truths of Applying Credit Card
•
Everyone is easy to apply for the credit cards.
•
One existed card applied for another cards
without verification in promotion campaign.
•
Platinum card holders are everywhere in Taiwan.
•
Most financial institutions focus on the prior
process of credit card verification instead of the
posterior process of the risk management after
cards issued.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Introduction
What the Card Issuers Need ?
•
Credit risk management is critical safeguard
against the possible losses.
•
A credit risk management alert system will be
able to freeze the credit usage or to reject the
on

going transaction and to prevent the potential
bad debts over the credit limit.
•
Banking industrial need to construct an efficient
credit risk prediction system to detect the default
of card holders correctly.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Introduction
Research Work in Credit Assessment
•
Some researches applied trandional statistic regression
models such as Orgler(1970) Steenackers
＆
Goovaerts
(1989)
•
Many method in statistics ,such as regression
analysis ,variance analysis and principal component
require a large amount of samples and satisfy certain
probability distribution.
•
Recent studies use Artificial Intelligence (AI) methods for
credit assessment. Neural network is the more recently in
support of both business and financial applications.
•
Many applications of AI can be found in (Brause,
Langsdorf, and Hepp, 1999), (Aleskerov, Freisleben and
Rao, 1997), (West, 2000) (Donato et. al., 1999)
Innovative Computing on Finance, ICICIC2007
Conference session C17
Objective of the system
1.
The aim of this study is to construct an efficient
risk prediction system to detect the default of
credit card holders correctly.
2.
The system collects the personal and financial
information of credit card holders and then
applies evolutional neural network which
integrated with grey incidence analysis and
Dempster

Shafer theory of evidence to predict
the default cases and trace the behaviors of
the card holders and manage the default risks.
Innovative Computing on Finance, ICICIC2007
Conference session C17
System structure
Innovative Computing on Finance, ICICIC2007
Conference session C17
Research Methodologies
1.
Evolutional neural network
2.
Grey incidence analysis
–
Ju

Long Deng, 1998, Essential Topics on Grey System, Theory and
Application, China Ocean Press.
–
Kun

Li Wen, 2004, Grey System Modeling and Prediction, Yang’s
Scientific Research Institute, USA.
3.
Dempster

Shafer theory
–
G.. Shafer, “A Mathematical Theory of Evidence”, Princeton, NJ,
Princeton, University Press, 1976.
–
G.. Shafer, “Probability Judgement in Artificial Intelligence”,
Uncertainty in Artificial Intelligence. L. N. Kanal and J. F. Lemmer.
New York, Elsevier Science, 1986.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Evolutional neural network
Limitation of Neural Network Training
•
The back

propagation learning algorithm cannot
guarantee an optimal solution as it might
converge to a local optimal weights. As a result,
the neural network is often unable to find a
desirable solution to a problem.
•
The other difficulty is to selecting an optimal
topology for the neural network. The network
architecture for a particular problem is often
chosen by means of heuristics.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Evolutional neural network
Genetic algorithms
are an
effective optimisation technique
that can be applied to guide both
optimisation of weights and
topology.
‧‧‧‧
‧‧‧‧‧‧
‧‧‧‧‧‧
Set Up Parameters
(crossover rate)
0.2
(mutation rate)
0.04
(evolution steps)
1000
(population size)
20
(learning rate)
0.5
(monmentum
factor)
(0.8,0.9)
Innovative Computing on Finance, ICICIC2007
Conference session C17
Source: Negnevitsky, Pearson Education, 2002
Innovative Computing on Finance, ICICIC2007
Conference session C17
Evolutional neural network
Execution Step:
•
Step 1: Randomly generate an initial population
of chromosomes which represents the topology
of the neural networks.
•
Step 2: Calculate the fitness of each individual
chromosome.
•
Step 3: Create a pair of offspring chromosomes
by applying the genetic operations such as
reproduction,
crossover and mutation
operations.
•
Step 4: Replace the initial chromosome
population with the new population.
•
Step 5: Go to Step 2, and repeat the process
until the termination criterion is satisfied.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Grey incidence analysis
1.
The fundamental idea of the grey incidence
analysis is that the closeness of a relation is
judged based on the similarity level of the
geometrical patterns of sequence curves. The
more similar the curves are ,the higher degree of
incidence between sequence.
•
Generation technique of grey Sequences
: to
realize the data pretreatment with analysis of
object system and applying operators of
sequences.
•
Grey incidence analysis techniques
: to find
out relationship of sequences based on the
geometry comparability of these sequences.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Grey incidence analysis
2.
Execution Step:
•
Step 1: Transform each sequence to grey
generation sequences by four techniques.
•
Step 2: Calculate incidence coefficient and
degree of grey incidence. Assume that the
following sequence
x
0
representing the
characteristics of a system.
•
And the following is the sequence of relevant
factors.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Grey incidence analysis
•
The degree of grey incidence
γ(x
0
, x
i
)
is denoted
as
γ
0,i
and the incidence coefficient
γ(x
0
(k), x
i
(k))
at the point of the sequence as
γ
0,i
(k).
•
For
ζ
(0, 1)
, where
ζ
is called distinguishing
coefficient.
•
γ
(x
0
(k), x
i
(k))
, define
Innovative Computing on Finance, ICICIC2007
Conference session C17
Grey incidence analysis
•
The degree of grey incidence
γ(x
0
, x
i
)
can
be calculated as the following Average
approach.
•
Step 3: The order of grey incidences is
defined as the following according to their
values.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
The Dempster

Shafer decision theory is considered a
generalized Bayesian theory which is traditional
method to deal with statistical problems.
•
The
Dempster

Shafer theory
is a mathematical
theory of evidence based on belief functions and
plausible reasoning, which is used to combine
separate pieces of information (evidence) to calculate
the probability of an event.
•
The Dempster

Shafer (D

S) theory of evidence was
created by Glen Shafer [Shafer, 1976] at Princeton.
He built on earlier work performed by Arthur P.
Dempster. The theory is a broad treatment of
probabilities, and includes classical probability and
certainty factors as subsets.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
Consider the nature of evidence.
•
Some evidence is not reliable (the weatherman is
wrong sometimes and right sometimes).
•
Some evidence is uncertain (an intermittent
atmospheric reading).
•
Some is incomplete (the wind speed by itself does not
tell us much).
•
Some evidence is contradictory (the weatherman's
forecast and the atmospheric conditions).
•
Some evidence is incorrect (a broken atmospheric
data source or a wrong weather forecast).
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
In the D

S theory of evidence, the set of all
hypotheses that describes a situation is the frame of
discernment. The hypotheses should be mutually
exclusive and exhaustive, meaning that they must
cover all the possibilities and that the individual
hypotheses cannot overlap.
•
The D

S theory mirrors human reasoning by narrowing
its reasoning gradually as more evidence becomes
available. Two properties of the D

S theory permit this
process:
–
the ability to assign belief to ignorance
–
the ability to assign belief to subsets of hypotheses.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
Two special sets applied in D

S theory. The first is the
null set, which cannot hold any value and the second
special set is a set contains all elements. Assigning
belief to the second set does not help distinguish
anything and representing ignorance. Humans often
give weight to the hypothesis "I don't know", which is
not possible in classical probability. Assigning belief to
"I don't know" allows us to delay a decision until more
evidence becomes available.
•
Each data source,
S
i
for example, will contribute its
observation by assigning its beliefs. This assignment
function is called the “probability mass function” and
denoted by
m
i
. So, the upper and lower bounds of a
probability interval can be defined as contains the
precise probability of a set of interest in the classical
sense, and is called
belief
and
plausibility.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
The lower bound of the confidence interval is
the belief confidence, which accounts all
evidences
E
k
that support the given
proposition “A”:
•
Belief
i
(A) =
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
The upper bound of the confidence
interval is the plausibility confidence,
which accounts all the observations that
does not rule out the given proposition:
•
Plausibility
i
(A) =
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
For each possible proposition (e.g., A),
Dempster

Shafer theory gives a rule of
combining data source
S
i
’s observation
m
i
and data source
S
j
’s observation
m
j
:
Innovative Computing on Finance, ICICIC2007
Conference session C17
Dempster

Shafer theory
•
The Dempster's rule of combination, is a
generalization of Bayes' rule. This rule strongly
emphasises the agreement between multiple
sources and ignores all the conflicting evidence
through a normalization factor.
•
Compared with Bayesian theory, the Dempster

Shafer theory of evidence is much more
analogous to our human perception

reasoning
processes. Its capability to assign uncertainty or
ignorance to propositions is a powerful tool for
dealing with a large range of problems that
otherwise would be intractable.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Experiment Results
Data Processing
•
The raw data are segmented into good records
and bad records for two successive terms and
then are randomized to improve the
performance of the training process.
•
To provide sufficient and adequate data for the
system evaluation, total of 4000 records are
collected and subdivided into 1000 for the
training set and 3000 for the cross validation set.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Experiment Results
•
Minimum Payment Due (X21)
•
Last Minimum Payment (X23)
•
Gender (X07)
•
Number of Cards Held (X04)
•
Martial Status (X08)
•
Card Holder’s Age (X05)
•
Revolving Credit (X17)
•
Account Duration (X01)
•
Available Credit (X20)
•
Annual Income (X10
Among 24 explanatory variables , it is found that a total
of 10 variables have higher ranking derived from the
integrated model.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Experiment Results
Result of the feature selection
Rank
Traditional
GIA (1)
Traditional
GIA (2)
Modified
GIA (1)
Modified
GIA (2)
Integrated
Model
1
X02
X19
X19
X19
X21
2
X23
X01
X01
X01
X23
3
X21
X21
X21
X21
X07
4
X17
X04
X23
X04
X04
5
X16
X07
X04
X07
X08
6
X11
X23
X07
X23
X05
7
X12
X18
X08
X18
X17
8
X13
X08
X05
X08
X01
9
X15
X05
X18
X05
X20
10
X14
X20
X20
X20
X10
GIA: Grey Incidence Analysis
Innovative Computing on Finance, ICICIC2007
Conference session C17
Experiment Results
Comparison of prediction accuracy
Prediction
Accuracy
% of correct
predictions
No. of wrong
predictions
Evaluation
Periods
This
Term
Next
Term
This
Term
Next
Term
Evolutional Neural
Network Only
77.37%
74.73%
226
253
Feature Selection
(GIA)
82.70%
80.16%
173
199
Feature Selection
(DS)
86.33%
82.47%
137
176
GIA: Grey Incidence Analysis
DS: Dempster

Shafer Theory
Innovative Computing on Finance, ICICIC2007
Conference session C17
Conclusion
•
We have found this integrated feature selection
approach performs better than that of applying grey
incidence analysis only in terms of the rate of prediction
accuracy.
•
The former correctly predicts the default cases to an
average of nearly 86.33% of all cases, which is about
3.63% higher than the latter. As both methods results in
different order for the variables, the DS method is able to
combine the different outcomes of the grey incidence
analysis and perform the task of data fusion.
•
We discovered that using grey incidence analysis leads
us to the reduction of the variables during the process of
feature selection and understood that more additional
variables can not improve the accuracy of the perdition.
Innovative Computing on Finance, ICICIC2007
Conference session C17
Conclusion
•
This study also shows evolutional neural network with
feature selection (GIA) is superior to the evolutional
neural network with no feature selection. The former
correctly predicts the default cases to an average of
nearly 82.7% of all cases, which is about 5.4% higher
than the latter.
•
This study collected the real data from only one financial
institute to evaluate the performance of the integrated
model. Further research could follow this line to collect
more real data from other financial institutions located in
different geographic regions and investigate whether
there is different ranking priority with the input variables
and produce the inconsistent results with this study.
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