=Paper=
{{Paper
|id=Vol-2631/paper20
|storemode=property
|title=The Application of Weighted Decision Matrix for the Selection of Non-state Pension Provision Strategy
|pdfUrl=https://ceur-ws.org/Vol-2631/paper20.pdf
|volume=Vol-2631
|authors=Ryszard Pukała,Nataliya Vnukova,Svitlana Achkasova,Oleksii Gorokhovatskyi
|dblpUrl=https://dblp.org/rec/conf/momlet/PukalaVAG20
}}
==The Application of Weighted Decision Matrix for the Selection of Non-state Pension Provision Strategy==
https://ceur-ws.org/Vol-2631/paper20.pdf
The Application of Weighted Decision Matrix for the
Selection of Non-state Pension Provision Strategy
Ryszard Pukała 1[0000-0002-2943-8482], Nataliya Vnukova 2[0000-0002-1354-4838], Svitlana Ach-
kasova 2[0000-0001-7233-0189] and Oleksii Gorokhovatskyi 2[0000-0003-3477-2132]
1 The Bronisław Markiewicz State Higher School of Technology and Economics,
16 Czarnieckiego Str., Jarosław, 37-500, Poland
2 Simon Kuznets Kharkiv National University of Economics,
9-A Nauky Ave., Kharkiv, 61166, Ukraine
ryszard.pukala@interia.pl, vnn@hneu.edu.ua,
svitlana.achkasova@hneu.net, oleksii.gorokhovatskyi@gmail.com
Abstract. In this paper, it was proposed to justify the selection of a non-state
pension provision strategy, which takes into account the possibility of using the
limited financial resources of potential participants of the non-state pension sys-
tem. The criteria to choose the appropriate non-state pension provision entity as
well as the criteria to choose the priority association of non-state pension entities
were justified. The solution of these problems with the automatic decision mak-
ing tool known as a weighted decision matrix that is simple to implement and
understand was proposed. Additionally, it was proposed a method, which extends
the functionality of decision making with the estimation of the stability of the
decision made. It was denoted the decision to be confident if there is no oppor-
tunity to change one or two criteria weights and alternative coefficients and get a
totally different decision. The modeling has shown that the usage of a weighted
decision matrix allows making the decisions for complex tasks with a lot of cri-
teria and weights in a fraction of a second.
Keywords: Weighted Decision Matrix, Entity Association, Non-state Pension
Provision, Decision Making.
1 Introduction
Updating the issues of forming an additional non-state part to the state pension in-
creases the importance of a professional multi-criteria selection of a strategy for the
accumulation of funds in the system of voluntary funded pension provision (non-state
pension provision).
A strategic approach to the accumulation of funds in the voluntary retirement pen-
sion system is to choose the strategy (in the long term) that best serves the interests of
potential participants in the non-state pension system.
Copyright © 2020 for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
The development of the non-state component of the pension provision among the
working population is conditioned by the presence of economic and social precondi-
tions, in particular the deficit of the Pension Fund of Ukraine, the number of retirees,
etc.
The introduction of the second level of the pension system of Ukraine – the system
of mandatory funded pension provision, which is at the stage of initiation by the state
regulatory and supervision bodies, through the development of the draft Law of Ukraine
"On Mandatory funded pension provision" is an element of the reform of the pension
system of Ukraine. Approval of the second level of the pension system in the future
will complement the existing solidarity pension system of Ukraine with a new, manda-
tory savings account, in which working citizens will make payments to an individual
savings pension account [1].
So the prospects of the pension system of Ukraine are [1, 14]:
the development of non-state (voluntary) component;
the formation of a mandatory funded pensions system (obligatory) that complements
the existing solidarity pension system.
The development of a system of funded pension provision generally depends on the
level of financial support of potential clients. This development also depends on the
potential clients' understanding of the need to protect and expedient the formation of an
additional state pension, the availability of non-state pension services, the development
of alternative strategies for securing a future non-state pension.
Therefore, the issue of finding technical solutions in order to improve the efficiency
of decision making for customers of entities providing services of non-state pension
provision as a basis for the development of private pensions, and thus the basis for
future additional benefits and select the best option strategy allocation of these funds.
2 Related Work
A wide range of issues related to the functioning of entities providing services of non-
state pension provision and the development of the non-state pension system have been
investigated by Messacar D. [2], Zelenko N. [3], Haiduk I. [4], Malyshko Ye. [5],
Tkachenko N. [6], Smovzhenko T. [7], Iaroshenko O. [8] and others. These authors
have identified the peculiarities of the functioning of entities providing non-state pen-
sion and the selection of these entities, taking into account these characteristics.
According to the authors, mentioned above, it is advisable to try to find a way to
simplify the decision-making process by participants when choosing strategies for non-
state pension provision.
It should be noted that the effectiveness of the formation of the additional (non-state)
pension depends on the level of state regulation and supervision of the non-state pen-
sion provision entities; the ability to invest effectively (for example, low-risk invest-
ment instruments).
The development of the non-state pension component depends mainly on the level
of trust of participants to the entities providing services of non-state pension provision,
since there is a limited mechanism for guaranteeing the return of the invested funds.
For banks (entities providing services of non-state pension provision) the Deposit Guar-
antee Fund guarantees to each depositor of the bank the repayment of funds on his
deposit, reimburses the funds in the amount of the deposit, including interest, as of the
day of the beginning of the procedure of withdrawal of the bank from the market, but
no more than the amount of the maximum value of the deposit repayment on that day,
regardless of the number of deposits in one bank. The value of the deposit limit may
not be less than 200,000 UAH, according to source [9].
In full agreement with the opinion of H. Mintzberg [10], the authors consider a stra-
tegic plan that integrates the main goals of a financial institution, its policies, and ac-
tions into one.
A properly formulated strategy allows the ordering and allocation of always limited
resources in a highly efficient manner [10]. That is why the selection of a non-state
pension strategy that takes into account the ability to use the limited financial resources
of potential participants of the non-state pension system to maximize the additional
pension to the state (non-state) pension is relevant, and the use of a decision support
system will facilitate this process.
Ye. Malyshko identified the following criteria for choosing financial strategies for
non-state pension provision by business entities: diversity of pension programs; risk of
loss of contributions; reliability of financial instruments; activity monitoring; state con-
trol [5]. Also determined that the cluster (insurance companies, non-state pension funds,
banks, and business entities) is a priority (priority by weight ratio was 0.448). This
strategy is considered as the interaction of elements of a complex system that will allow
reconciling the interests of competing financial institutions and set the directions of
financial strategies of private pension provision by business entities [5].
O. Dolhova mentioned that the criteria for choosing a non-state pension fund are
generally the same for all financial institutions. The scientist has identified two direc-
tions: first, the criteria related to the rational perception of non-state pension entities,
covering the history of profitability and success of the non-state pension fund, as well
as the lifetime of a particular fund on the market; second, the criteria that have more
emotional connotations: this is the quality of customer service and reliability infor-
mation, as well as the various recommendations of stakeholders. Another important
criterion for selecting a fund is accessibility, which is difficult to secure without an
effective marketing policy [11].
According to O. Khudolii, one of the main criteria that attract investors when choos-
ing a non-state pension fund is the effectiveness of its activity, which is characterized
by an increase in the value of participants' contributions due to the investment activity
of the fund [12].
According to the Law of Ukraine “On implementation of lifetime retirement pro-
grams” Art. 9 identifies the peculiarities of the selection of a non-state pension fund by
an entity and other persons for the implementation of a pension program for which the
entity (employer) selects a non-state pension fund, concludes a pension contract and
pays pension contributions in the amount established by the program for the benefit of
employees -participants of the program who are members of the fund under this pension
contract [13].
The contribution of the paper includes:
an improved approach to choose a priority strategy for non-state pension provision
in Ukraine, which, unlike the existing ones, uses the weighted decision matrix as an
automatic decision making tool;
the practical application scope of the traditional WDM method has been expanded
with the novel module, that allows to measure the confidence level of the decision
being made.
3 Selection of Non-state Pension Provision Strategy
The criteria and procedures for selecting a non-state pension fund for the implementa-
tion of the lifetime retirement program is established and applied solely by the parties
to the sectoral agreement (collective agreement), taking into account the requirements
of the Law of Ukraine “On implementation of lifetime retirement programs” [13]. This
confirms the urgency of finding a way to simplify the decision-making process of par-
ticipants in the selection of entities providing services of non-state pension provision.
According to the Law of Ukraine "On non-state pension provision" the entities
providing services of non-state pension provision are: non-state pension funds through
the conclusion of pension contracts between pension fund administrators and contribu-
tors of such funds; life insurance companies by concluding life insurance contracts with
members of the fund, ensuring the risk of disability or death of the fund member; bank-
ing through the conclusion of agreements on the opening of pension deposit accounts
for the accumulation of pension savings within the amount determined for repayment
of deposits by the Deposit Guarantee Fund [14].
According to the authors, it is advisable to base this set of criteria on the selection of
an already appropriate non-state pension provision entity. The selection of strategies
should be based on the list of criteria (accessibility, diversification, economic effi-
ciency) and the range of possible strategies by different associations of entities provid-
ing services of non-state pension provision (non-state pension funds, life insurance
companies, banks, following the Law of Ukraine "On non-state pension provision"
[14]), which is presented in Table 1, formed based on sources [5, 8 – 12, 14].
As one can see from Table 1, the proposed strategies collectively shape the approach
to prioritizing a potential non-state pension strategy for a potential participant.
Table 1. Characteristics of non-state pension strategies
Strategy #1 Strategy #2 Strategy #3
Non-state pension Non-state pension Association of entities providing services
monosubject (only polysubjects (two or of non-state pension provision regardless
one non-state pen- more non-state pen- of number (non-state pension fund, life in-
sion fund, or only sion funds, or two or surance company and a bank; non-state
one life insurance more life insurance pension fund and life insurance company;
company, or only companies, or two or life insurance company and a bank; non-
one bank) more banks) state pension fund and a bank)
4 Weighted Decision Matrix Method (WDM)
A lot of different methods [15] to solve multi-criteria decision analysis (MCDA) prob-
lems in diverse scientific and practical applications (e.g. the choice of solar collector
structure [16], assessment of the environmental impact of different types of vehicles
[17]) were proposed previously.
The Weighted Decision Matrix (WDM) [18] is used in the research as a simple tool
to compare alternatives according to multiple criteria with importance level assigned to
each criteria.
Let us denote the quantity of strategies as M and the quantity of criteria as N . The
decision matrix size of M N contains the coefficients xij , i 1, M , j 1, N , that
measure the importance of each criteria for each strategy. Additionally, each criteria
has its own significance level wi , i 1, M . The importance of criteria is measured ac-
cording to five-level Likert-type scale from "Low" to "High", in a similar way like it is
done in Decision Making Helper software [19]. The coefficients xij may get values in
range [5;5] . Typically, wi and xij values are assigned by the experts in correspond-
ing fields.
Summary scores for strategy i are calculated according to:
M N
Si x w , i 1, M , j 1, N
i 1 j 1
ij , i (1)
following by the normalization with:
Si
S i , (2)
Tmax
where Tmax – is the maximum theoretically available score, Tmax N wmax xmax ,
wmax xmax 5 as was mentioned above.
Numerical values wi and xij for strategies 1-3 (Table 1) and 3 criteria (accessibil-
ity, diversification, effectiveness) are the following:
5 4 3
W (4,4,5), X 1 4 5 ,
3 4 5
where wi W , xij X , i – is the number of criteria (row), j – is the number of strat-
egy (column). All numerical coefficients here and below (in Tables 2-4) are provided
by the expert committee from 5 persons of the Banking and Financial Services depart-
ment of Simon Kuznets Kharkiv National University of Economics.
The results after the applying WDM approach based on (1) and (2) are shown in Fig.
1. It was defined 3 types of strategies (they are shown in Table 1) for non-state pension
provision. The decision on the use of strategy #3 (association of entities providing ser-
vices of non-state pension provision regardless of number (non-state pension funds and
life insurance company as well as a bank; non-state pension funds and life insurance com-
pany; life insurance company and a bank; non-state pension fund and a bank) is a positive
that can be taken into account either by a financial adviser or by a potential participant in
the non-state pension system when making appropriate decisions. The analysis suggested
by the authors of the criteria and strategies is consistent.
Non-state pension strategies
Strategy #3 76%
Strategy #2 69%
Strategy #1 52%
0% 20% 40% 60% 80%
Fig. 1. The results of WDM application to select a strategy for non-state pension provision
Based on sources [5, 8 – 12, 14], the criteria for choosing a priority association of non-
state pension entities (according to strategy #3) by a participant and their weights are
given in Table 2.
As one can see from Table 2, according to the results of weighting for each selection
criterion of a participant of an association of entities providing services of non-state
pension provision (according to strategy #3), the most priority selection criteria are
those that have a weight of 5, in particular: the effectiveness of asset management the
entity/entities providing services of non-state pension provision; availability of guaran-
tees for the return of accumulated pension funds; requirements for the minimum amount
of contribution from the participant; the variety of pension programs for the participant;
the possibility of early termination of a pension contract, or a life insurance contract or
a deposit agreement (pension) without financial losses.
Four alternatives are considered to select the priority association of entities (pro-
posed based on sources [5, 14]):
─ non-state pension fund, life insurance company and a bank (Alternative #1);
─ non-state pension fund and life insurance company (Alternative #2);
─ life insurance company and a bank (Alternative #3);
─ non-state pension fund and a bank (Alternative #4).
The weights X of corresponding criteria for all alternatives, assigned by expert assess-
ment, are presented in Table 3.
Table 2. Selection criteria for priority association of entities providing services of non-state
pension provision (according to winning strategy #3)
# Criteria Weight
1 The effectiveness of asset management the entity/entities providing ser-
5
vices of non-state pension provision
2 The availability of guarantees for the return of accumulated pension funds 5
3 The requirements for the minimum contribution fee from the participant
5
of non-state pension provision
4 A variety of retirement programs for the participants of non-state pension
5
provision
5 The possibility of early termination of a pension contract, or an insurance
5
contract, or a deposit agreement (retirement) without financial losses
6 The financial status of the entity/entities providing services of non-state
4
pension provision
7 The transparency of the activities of the entity/entities providing services
4
of non-state pension provision
8 The availability of advertising for the entity/entities providing services of 4
non-state pension provision
9 The possibility of consulting a participant of non-state pension provision 4
online
10 The reputation of the entity/entities providing services of non-state pen- 3
sion provision among clients
11 The reputation of the entity/entities providing services of non-state pen- 3
sion provision among other entities of non-state pension provision
12 The existence of an internal risk management system, including risks of 3
financial monitoring for the entity/entities providing services of non-state
pension provision
13 The existence of violations established by regulators for the entity/entities 3
providing services of non-state pension provision
14 The place of entity/entities providing services of non-state pension provi- 2
sion in the ratings (by the size of assets, number of participants, etc.)
15 The stage of the life cycle of the entity/entities providing services of non- 2
state pension provision
16 The availability of the contract between the participant and the entity/en- 2
tities providing services of non-state pension provision, territorial location
17 The level of professional competence of employees of the entity/entities 2
providing services of non-state pension provision
18 The participation of the entity/entities providing services of non-state pen- 2
sion provision in professional associations of financial institutions
Table 3. Coefficients of importance criteria for all alternatives
Criteria coefficient
Alternative
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
#1 4 4 3 5 4 4 4 4 4 4 4 4 3 4 4 3 4 4
#2 4 3 4 4 4 4 5 5 5 5 5 5 4 5 5 4 5 5
#3 3 4 3 4 3 3 4 4 4 4 4 4 3 5 4 4 4 4
#4 4 5 3 3 5 3 4 4 4 4 4 4 3 4 4 4 4 4
WDM was applied to make the decision about the choice of the most preferred alterna-
tive, the chart with results is presented in Fig. 2. As one can see, it is preferable to bring
together entities that provide non-state pension provision provided by a non-state pen-
sion fund and a life insurance company (Alternative #2).
Associations of non-state pension entities
Alternative #4 53%
Alternative #3 52%
Alternative #2 61%
Alternative #1 55%
45% 50% 55% 60% 65%
Fig. 2. The results of WDM application to select the priority association of entity in terms of
strategy #3
WDM method was also applied for the initial set of strategies, mentioned in Table 1
and criteria from Table 2. Corresponding expert importances are shown in Table 4.
Table 4. Coefficients of importance criteria for all strategies
Criteria coefficient
Strategy
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
#1 3 4 3 3 5 4 3 4 4 5 5 3 3 3 3 3 3 4
#2 4 5 4 4 4 4 4 5 4 4 4 4 4 4 4 4 4 5
#3 5 4 3 5 3 5 4 5 5 4 4 4 4 5 4 4 4 5
The results of the application of WDM method are presented in Fig. 3. These results
correspond to previous ones in Fig. 1, which means that the expert estimations are cor-
rect for both cases.
Non-state pension strategies
Strategy #3 60%
Strategy #2 58%
Strategy #1 51%
45% 50% 55% 60% 65%
Fig. 3. The results of WDM application to select the strategy for non-state pension provision (by
18 criteria)
5 Confidence estimation
Sometimes, it is not possible to understand whether the decision, provided by decision
making systems is confident or not. Often the solution of this problem comes from some
manual artificial threshold that allows distinguishing different levels of confidence,
which is not convenient enough.
The decision is suggested to be the confident one, if it is not possible to find such
pair of weight ŵ and coefficient x̂ changing which immediately leads to the change of
the global decision. If it is possible to find such pair it means that the common decision
may depend only on just some particular expert value.
Let's denote S1 as the best score, calculated according to (1)-(2), and S 2 as the sec-
ond best score. Corresponding weighted vectors without the summarization are
s1 x11, w1 , x12, w2 , .., x1N , wN and s2 x21, w1 , x22, w2 , .., x2 N , wN , where N is the
quantity of criteria.
The weighted difference between two best decisions is D T max(S1 S2 ) , it is al-
ways positive because S1 S 2 . Elements of vectors s1 and s2 are compared one by
one in turn, searching for the way to compensate the required D value with increasing
of x2i or wi or even both of them. Only the increasing values of the second best strat-
egy were considered here in the effort to improve it. The reverse approach with the
decreasing of corresponding coefficients x1i and weights wi of the winning strategy is
possible too. The pseudocode to implement this search is below.
Calculate D and weighted vectors s1 and s2
Set N as the quantity of weights
Set X as the coefficients matrix, X[0,:] is the best
strategy coefficients, X[1,:] is the second best strategy
coefficients, etc.
Set W as the criteria weights vector
Iterate I from 0 to N:
Calculate the difference between pair d = s1[i]-s2[i]
If d > 0: // attempt to increase s2
If d > D: // if that's enough to compensate
Current coefficient = X[1,i]
Current weight = W[i]
Find such a combination of new coefficient
and weight (changing one of them firstly, both if re-
quired) that allows to increase current product at a
value, that is bigger than d
If new coefficient and/or new weight is
found:
Update X[1,i] = new coefficient
Update W[i] = new weight
Stop calculations if there is enough to
find just one change
Let's consider the example of how this measurement of the confidence works. The
weights, provided in Table 2 are used together with and a bit modified (compared to
Table 3) coefficients, provided in Table 5.
Table 5. Modified coefficients of importance criteria for all alternatives
Criteria coefficient
Alternative
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
#1 5 4 4 4 4 4 4 5 5 5 5 4 3 4 4 3 4 4
#2 4 4 5 5 3 4 5 4 3 4 4 5 4 5 5 4 3 3
#3 3 4 3 4 3 3 4 4 4 4 4 4 3 5 4 4 4 4
#4 3 5 3 3 5 3 4 4 4 4 4 4 3 4 4 4 4 4
Scores vector after the WDM was applied is S (0.59, 0.58, 0.52, 0.53) , so the first
alternative is the best one. The difference between the highest and the second highest
is just 0.01, so, there is a question if this distance is valuable enough or not.
The application of confidence analysis, described above, shows, that the change of
the only coefficient #9 for the second alternative from 3 to 5 (it is marked with bold in
Table 5) immediately leads to the change of the scores vector to
S (0.59, 0.6, 0.52, 0.53) and the second alternative becomes the best one. In this case
the decision is considered not to be confident. Of course, such analysis is possible not
only for first and the second best scores, but for any pair.
It is worth mentioning, that only the decision that is shown in Fig. 2 is confident, the
decisions, presented in Fig. 1 and Fig. 3 are not.
Increasing the number of selection criteria complicates the decision-making process
of a potential client of an entity engaged in providing non-state retirement benefits, but
the results witch obtained did not significantly affect the priority of the third strategy.
The decision will be positive for strategy #3.
6 Conclusion
The paper proposes the solution of the problem related to the choosing a priority strat-
egy for non-state pension provision. This research proposes the usage of the decision
making system commonly known as Weighted Decision Matrix, which is simple
enough to implement.
The selection of the appropriate non-state pension provision entity is based on three
criteria: accessibility, diversification and economic efficiency. Three strategies are con-
sidered as alternatives and it was found, that association of entities providing services
of non-state pension provision regardless of number is the best choice.
The criteria for choosing a priority association of non-state pension entities amongst
four alternatives were proposed. It was found, that non-state pension funds and life
insurance companies are the best alternatives.
Additionally, the module that complements weighted decision matrix decision mak-
ing method is proposed. It allows to understand, whether the final decision is confident
or not. The decision is suggested to be stable (confident), if that is not possible to change
just a single value or pair of criteria weights or expert coefficients for alternatives which
leads to a different decision.
The practical value of the work is the usage of automatic WDM tool following by
the confidence analysis of the decision which has been applied for the solution of the
problem of the choice strategies for private pension provision and entities that provide
these services.
The comparative analysis of WDM and another multi-criteria decision methods (e.g,
TOPSIS, AHP) for solving of the non-state pension provision strategy selection could
be the topic for future research.
Acknowledgments
This research was supported by The Ministry of Education and Science of Ukraine
is the scope of the fiscal theme No. 45/2020–2021 “Formation of a risk-oriented system
of funded pension provision” (0120U101508) which is performed in Simon Kuznets
Kharkiv National University of Economics.
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