Fuzzy approach based money laundering risk assessment

Full text

Fuzzy approach based money laundering risk assessment
M¯aris Krasti¸nˇs
Department of Mathematics, University of Latvia, Jelgavas iela 3, Riga, Latvia
Institute of Mathematics and Computer Science, Rai¸na bulv¯aris 29, Riga, Latvia, mk18032@lu.lv
Abstract
This paper introduces solution for numeric
evaluation of money laundering risk contain-
ing several different risk factors. For this
purpose we consider the options for aggre-
gation of risk factors and obtaining consol-
idated risk level. The proposed models are
constructed using maximum t-conorm and
Lukasiewicz t-conorm. Practical example is
provided for calculation of consolidated client
money laundering risk score.
Keywords: Money laundering risk, ag-
gregation operators, maximum t-conorm,
Lukasiewicz t-conorm.
1 Introduction
Over the last two decades the risk assessment meth-
ods and tools have been widely developed for different
purposes. The financial industry has been just one,
yet important, end user of the risk assessment solu-
tions. While such risks as the credit risk, the finan-
cial risk and the liquidity risk have always had a solid
statistic basis for numerical calculations and applica-
tion of the probability theory, supervisory authorities
have increased their expectations and demands for in-
troducing mathematical models for assessment of the
compliance risk, including the risk of money launder-
ing, which lacks any solid mathematical background
and can rely on expert opinions only. At the same
time it should be noted that the number of subjects to
Anti Money Laundering (AML) laws has significantly
increased over the last decade. Therefore the models
for scoring of money laundering risk often shall be im-
plemented not only by financial institutions, but also
by real estate brokers, gambling companies, notaries
and other obliged entities pursuant to applicable AML
laws.
The leading global AML software providers have de-
veloped different technological solutions to cope with
increasing legal demands for scoring and monitoring of
customers and their transactions. However, the con-
tents of these solutions are not openly disclosed to a
wider audience, and so far there have been very few at-
tempts in proposing the models for money laundering
risk assessment in scientific publications. The review
article [5], published in February 2018, summarizes all
efforts used so far in finding the most appropriate ap-
proach for efficient handling of tasks related to preven-
tion of money laundering and highlights importance of
the detection of suspicious transactions. However, it
is evident from the practical point of view that trans-
actional patterns are just consequences from engaging
into business with particular customers posing lower or
higher risk of money laundering. A use case provided
in [4] allows to cope with a very simple transactional
pattern, but it is important to take into account the
customer specifics as part of so called Know Your Cus-
tomer (KYC) process as mentioned also in [5].
The main goal of the KYC process is to implement a
robust solution allowing the obliged entities to assess
the level of money laundering risk as part of the cus-
tomer relationship establishment, often referred as an
on-boarding process. The customers shall disclose dif-
ferent qualitative and quantitative data which can be
afterwards evaluated by experts and transposed into
risk factors with corresponding risk levels. Aggrega-
tion of these risk levels results in the risk scores. Dif-
ferent scales can be used for this purpose, but we will
apply the fuzzy numbers and assign the values close to
0 for the lowest risks, and the values close to 1 for the
highest risks. It shall be noted that some risk models
are inverted by assigning the values close to 1 for the
lowest risks, and the values close to 0 for the highest
risk. Depending on the resulting money laundering
risk scores obliged entities are required to apply risk
mitigation actions, which include, but are not limited
to regular monitoring of customer transactions, ob-
taining relevant documentation on customers’ source
of wealth and source of funds etc.
11th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2019)
Copyright © 2019, the Authors. Published by Atlantis Press.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Atlantis Studies in Uncertainty Modelling, volume 1
610

The paper considers several options for risk level aggre-
gation of such risk factors as customer residence, occu-
pation or business for legal entities, customer reputa-
tion, estimated volumes and values of transactions and
other similar factors as selected by the obliged entity
or required by applicable laws and regulations. Sec-
tion 2 provides an overview of aggregation principles
which are further analysed by considering application
of maximum t-conorm in Section 3 and Lukasiewicz t-
conorm in Section 4. Combination of these t-conorms
is proposed in Section 5. A practical example of risk
levels’ aggregation based on expert evaluations is pre-
sented in the Section 6.
2 Conditions for aggregation of risk
factors in money laundering risk
assessment model
The risk is usually considered as a function of prob-
ability and impact or likelihood and severity. Such
definition is suitable for many industries as outlined,
for example, in [6, 7]. It also allows application of
Mamdani-Type or Sugeno-Type fuzzy inference sys-
tems for obtaining the consolidated risk levels as de-
scribed by [1, 11, 9]. This process is similar to different
other practical applications provided in [2].
Contrary to the previous examples of risks, money
laundering risk attributed to each customer is rather
specific and embraces comparably vague component
of severity, which can be hardly characterised by any
numeric value. It particularly applies to such indica-
tors as reputational impact or business sustainability.
At the same time AML laws and regulations require
implementation of detailed KYC procedures and as-
sessment of multiple risk factors for each customer.
Therefore an expert opinion is among the most appro-
priate solutions for assigning the risk levels for corre-
sponding notional risk factors. A simple example can
be used to explain the need for a human decision in
assessing the risk level. Let us consider two companies
of different size and their estimated average transac-
tion values. While EUR 100 000 payment would be
treated as low risk indicator with value close to 0 for
the large company, it would be definitely a high risk
indicator with value close to 1 for the small company.
Similar judgement is valid also for assessment of ex-
pected payment volumes which can be considered as
another different risk factor.
Let us consider that all risk levels of corresponding risk
factors Xk, k ∈ {1, ..., i}and k∈Nare expressed in
the form of fuzzy set µ= (x1, ..., xi), i ∈ {1, ..., n}and
n∈N. In order to aggregate these risk levels we will
use aggregation operator A:S
n∈N
[0,1]n→[0,1]. An
example of ten risk factors (i= 10) with correspond-
ing risk levels for two sample customers is provided in
Figure 1. It is evident that customers can be differ-
ent and with different risk levels for corresponding risk
factors, which are notional and do not correspond to
any particular values on xaxis.
The use of risk level fuzzy sets, especially their
Figure 1: Example of risk levels for two sample cus-
tomers
graphical representation, provides a good preliminary
overview of overall customer risk level. However, they
do not encompass importance of each risk factor, and
also do not provide a clear answer, if the obliged en-
tity is facing high or low risk customer. Therefore we
will explore the options for aggregation of risk levels
using different aggregation operators in order to ob-
tain the customer risk score. First of all we consider
application of different average operators analysed by
[3]. We define the fuzzy weighted average of risk levels
(x1, ..., xi) as follows:
W(x1, ..., xn) =
n
X
i=1
ωixi
where ωiare weights for each corresponding xiand
n
P
i=1
ωi= 1. At the first glimpse such approach could
be considered as suitable since the risk score is the
mean value of all weighted risk levels. However, due
to specifics of money laundering risk there are many
occasions when it is not reasonable to accept that the
risk score is lower than value of the highest risk level
in the fuzzy set µ= (x1, ..., xn). Therefore alternative
aggregation operators should be considered.
3 Aggregation of risk levels with
maximum t-conorm
As part of the risk level aggregation it can be as-
sumed that for particular cases the total risk level of
any sample customer cannot be lower than the high-
est (maximum) risk level of all risk factors. Therefore
we can apply the maximum t-conorm M(x1, ..., xn) =
max(x1, ..., xi), i∈ {1, ..., n}and n∈N. It should be
noted that all risk factors Xkmay not be equally im-
portant for customer risk scoring. Therefore we apply
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fuzzy coefficients ai∈[ 0,1] , i ∈ {1, ..., n}and n∈N
allowing to keep the values of certain initial risk levels
or decrease them in similar way as proposed by [10].
In our model
n
P
i=1
ai6= 1, and fuzzy coefficients can be
regarded as the indicators of risk appetite resulting
in the fact that particular risk levels are decreased, if
obliged entity considers them as less important. Con-
sequently the maximum t-conorm can be expressed in
the following format:
M(x1, ..., xn) = max(a1x1, ..., aixi),(1)
i∈ {1, ..., n}and n∈N.
When applying such aggregation, the most important
risk factors with corresponding risk levels are consid-
ered. However, other risk factors of lower importance
with non-zero risk levels should not be disregarded as
their aggregated impact could be more severe than the
highest risk level of the most important risk factor.
This implies that additional options for aggregation of
the risk levels of non-critical risk factors are required.
4 Aggregation of risk levels with
Lukasiewicz t-conorm
Aggregation using arithmetic sum often results in val-
ues exceeding 1. If we consider the example pro-
vided in Figure 1, it is evident that the sum of only
two particular risk levels for both sample customers
is greater than 1 while there are non-zero risk level
values for four more risk factors. In order to over-
come this problem, we apply Lukasiewicz t-conorm
L(x1, ..., xn) = min(1,
n
P
i=1
xi), n∈N. As in the case of
maximum t-conorm we note that the risk factors are
not equally important. Therefore we apply the same
fuzzy coefficients ai∈[ 0,1] , i ∈ {1, ..., n}and n∈N
for calibration of the risk level values. The adjusted
Lukasiewicz t-conorm is expressed as follows:
L(x1, ..., xn) = min(1,
n
X
i=1
aixi),(2)
n∈N. The formula (2) underlines the meaning of
coefficients aias values expressing the risk appetite.
It is evident that lower aimeans higher risk appetite,
and more risk factors can be included in the total risk
score unless it does not exceed the threshold of non-
acceptable risk as internally set by the obliged entity.
While Lukasiewicz t-conorm and formula (2) provide a
sound basis for suitable aggregation of money launder-
ing risk levels into single value risk score, such aggrega-
tion may decrease the importance of some critical risk
factors preserved in case of the maximum t-conorm.
There is another scenario when the obliged entity may
select some critical risk factors and benchmark their
risk levels against aggregated risk level values of the
remaining risk factors. Therefore construction of the
combined aggregation operator is proposed in the Sec-
tion 5.
5 Aggregation of risk levels with
combined t-conorm
Let us assume that we have to deal with some crit-
ically important risk factors and less significant risk
factors by splitting them in two groups and combining
results using the following t-conorm: C(x1, ..., xn) =
max(x1, ..., xk,min(1,
n
P
j=k+1
xj)), n∈N. Such t-
conorm is commutative, monotone, and the number
1 acts as its identity element. However, this t-conorm
is not associative as it basically consists of two inde-
pendent parts. From the practical point of view, it
is not critical that associativity does not hold. The
t-conorm Cis not unique in that sense, as there are
similar examples of functions, like copulas and quasi-
copulas analysed in [8], where associativity does not
hold.
When applying the combined t-conorm Cwe should
consider the same principle of the importance of risk
factors applied to maximum t-conorm and Lukasiewicz
t-conorm. The resulting formula will be the following:
C(x1, ..., xn) = max(a1x1, ..., akxk,min(1,
n
X
j=k+1
ajxj)),
(3)
n∈N. In practice (3) will allow to select the critical
risk factors out of the sum of remaining risk factors.
Such calculation is two folded. First of all it secures
that important high level risk factors are not missed,
and secondly it allows to benchmark aggregated level
of less important risk factors against critical risk fac-
tors.
6 Example of aggregated risk score
The main purpose of the proposed aggregation model
is to enable the end users, including obliged enti-
ties and supervisory authorities, to implement sim-
ple and clear solutions for obtaining the customer’s
money laundering risk score. In our example we
will use four risk levels and apply them to each
risk factor pursuant to the widely accepted interna-
tional standards: low risk, medium risk, high risk,
non-acceptable risk. Table 1 provides correspond-
ing intervals for each risk level. We will use a
sample customer A from Figure 1 with correspond-
ing fuzzy set of 10 risk levels µ= (x1, ..., x10) =
(0; 0,2; 0,6; 0,1; 0,9; 0; 0; 0,4; 0; 0,5). As the next step
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RISK LEVEL INTERVAL OF
RISK SCORE
Low [ 0, 0,30)
Medium [ 0,30, 0,60)
High [ 0,60, 0,95]
Non-acceptable ( 0,95, 1]
Table 1: Values of risk levels.
we will apply the following fuzzy coefficients char-
acterising importance of corresponding risk factors:
a1= 1, a2= 1, a3= 1, a4= 0,8, a5= 0,7, a6=
0,5, a7= 0,5, a8= 0,4, a9= 0,3, a10 = 0,2. In
such case (1) and (2) result in the following val-
ues: M= 0,63, L= min(1; 1,77) = 1. It means
that the maximum t-conorm returns the value slightly
above the lowest value of the high risk, while applica-
tion of Lukasiewicz t-conorm results in non-acceptable
risk. Therefore intuitively these values could indicate
that the most suitable level of aggregated risk score
could be high, but certainly lower than non accept-
able. In order to apply (3) we will select x1, x2, x3, x4
as the most critical risk factors. Such selection re-
sults in the following value of the combined t-conorm:
C= max(0,6; min(1; 0,89)) = 0,89. The result cor-
responding to high level risk (with risk score 0,89) is
quite suitable for the obliged entity with rather low
risk appetite. At the same time it should be admitted
that the risk appetite can be increased by modifying
fuzzy coefficients ai, and a5in particular.
7 Conclusions
The proposed methods for aggregation of risk levels en-
able efficient calculation of risk scores. While simple
t-conorms result in loss or overestimation of the im-
portance of corresponding risk factors, combination of
t-conorms provide a good basis for a simple risk scor-
ing. Transparency of the combined t-conorm can allow
supervisory authorities to identify the risk appetite of
any obliged entity which has chosen to apply such ag-
gregation model for obtaining money laundering risk
scores. Further research will focus on the fine-tuning of
the aggregation model and also introducing Mamdani-
Type or Sugeno-Type fuzzy inference systems towards
each risk factor of the money laundering risk.
Acknowledgement
Author is thankful for the partial support from the
project No LZP-2018/2-0338 ’Development of fuzzy
logic based technologies for risk assessment by means
of relation-grounded aggregation’ of the Latvian Coun-
cil of Science.
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