A Novel Prediction Model for

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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.