Pension funds governance: combining SD, Agent based
Modelling and fuzzy logic to adress Dynamic Asset and Liability
Management (ALM) problem
Ricardo Matos Chaim (rmchaim@yahoo.com.br)
Gettilio Vargas Foundation — Brasilia
Av. L2 Norte, Quadra 602 — Brasilia-DF, CEP 70.830-020 - Brasil
Tel: (61) 3225-9132/ 3226-0033
Fax: (61) 3226-0493 / 3225- 3960
Rosalvo Ermes Streit (rosalvo.streit @ gmail.com
Abstract
The governance is a system composed by a great number of interdependent entities,
with different degrees of relationship. This article considers the governance of a social-
economic and political environment under a pension fund’s perspective as a complex
system in which the interactions among the actors influence the governance and the
governance can influence their interactions, in a recursive way. In order to cope with the
peculiarities of complex systems, a system dynamics (SD) model, combined with an agent-
based model is proposed to analyze population dynamics and the influence of credibility as
a subjective factor over the expected adhesion of new participants. The behavior of the
agents is modeled using fuzzy logic. This way, the article aims to evidence the power of a
multi-paradigm model to study complex environments and to offer a way to address a
dynamic ALM problem in order to manage solvency and liquidity risks in pension funds.
Key words: Pension funds, Dynamic Asset and Liability Management (ALM), pension
schemes, fuzzy logic, agent based modeling, planning under uncertainty
Introduction
A dynamic ALM’s model problem is how to manage credit, market, operational and
image risks to estimate returns over long-term investments based on uncertain liabilities.
Thus, planning under uncertainty requires reliable tools to get better dynamic financial
analysis and to manage actuarial assumptions in order to set policies that assure good
solvency and liquidity to pension funds.
Lifetime and demographic studies focus on the population dynamics of a pension
fund that has, among others, rates of mortality, withdrawal, disability and retirement that
must be considered in assessing pensions costs and to consider credibility in structuring a
prospective cash flow. This way, the research conducted by the authors combine methods
and techniques to study pension funds population models and the influence of subjective
factors over it.
Thus, combining SD methods to agent-based modeling applies simulation to cope
some aspects of the social-economic and political environment under the pension fund
perspective, using fuzzy logic to model the behavior of the agents.
To place the issues into perspective, this paper has four sections. First, it observes
the complexity inherent to pension funds and some information about its governance. Next,
discusses a dynamic Asset and Liability Management (ALM) approach for pension funds.
Follows fuzzy logic rules model the agent’s behavior in a beliefs-desires-intentions (BDI)
agent architecture. Finally, in the conclusion, considerations about the combination of
system dynamics and agent based modeling, with summary comments about the
combination of methods to address subjective factors.
1 Complexity and governance
Edmonds (2003) stated that when a study domain is quite complex, the approaches
based on equations or on other analytical techniques are impracticable or even impossible
to be applied. In complex systems, the interactions between the parts may cause relevant
differences in system’s performance. Wagner (1986) argues that the result of the
combination of the uncertainty, the dynamic interactions, the subsequent events, and the
complex interdependences among system variables difficult the analysis of a problem.
According to Edmonds (2003), simulation is the only way to model the behavior of this
type of systems.
In order to cope with the peculiarities of pension funds, we propose the use of an
agent-based model to represent the behavior of the pension fund participants and the social-
economic and political environment to provide deeper insights by simulation experiments.
The agent-based models can help to clarify the agents’ interactions and behaviors (micro
level), e.g., the non-linear behaviors of the system that are difficult to be captured with
mathematical formalisms. In this case, a multi-agent model combined with a SD model will
aid to manage solvency and liquidity risks on a pension fund, called Dynamic Asset and
Liability Management (ALM). Therefore, in this study the proposed pension fund model is
a multi-paradigm simulation model. Each modeling approach supports some particular
representation of it.
The study of multi-agent systems started in the field of the distributed artificial
intelligence (DAI) about twenty years ago (Weiss, 1999). The precursor of these systems is
the object-oriented programming (OOP). The OOP objects keep their own data structures
and procedures (methods), and communicate to each other with messages. Artificial
intelligence works with computational aspects of intelligence and focuses on systems that
act separately.
The DAI, in turn, is the study, construction and the application of multi-agent
systems, which are systems where some intelligent agents interact and aim to reach a set of
goals or execute a sequence of tasks (Weiss, 1999). The term “intelligent agent” indicates
object with flexible autonomous capacity. Streit (2002), for example, evidences the
importance of the use of the DAI in social sciences study field and presents references of its
use in the organizational area.
According to Lempert (2002), the agent-based models can represent important
phenomena difficult to capture with mathematical formalisms. The author argues that these
models are distinguished for relating the heterogeneous behavior of the agents (different
information, different decision rules, and different situations) with the macro behavior of
the system. The agents have several interaction rules and, by simulation, it is possible to
explore the emergent behavior along the time and the space. This modeling technique does
not assume a unique component that takes decisions for the system as a whole. The agents
are independent entities that establish their own goals and have rules for the decision
making process and for the interactions with other agents.
The agents’ rules can be sufficiently simple, but the behavior of the system can
become extremely complex (Gilbert, 1995). Therefore, the complexity can emerge because
of simple rules in the level of the individuals. The emergence “occurs when the interactions
among objects at one level give rise to different types of objects at another level” (Gilbert,
1995, p.15).
The modeling process relates the representation of the system under analysis from
the real world to a model capable to describe similar behavior. Figure one shows that the
design of the computational model incorporates relevant aspects of the system that we want
to know. It is a formal representation of a conceptual model. The conceptual model, in turn,
is an abstraction of the real world under analysis.
nivel 3:
computational model
nivel 2:
conceptual model
nivel 1:
system under analysis.
Figure 1 - The modeling process.
The modeling process of an agent-based model defines its individual components,
as a bottom-up approach. The definition of the agents’ behaviors is extremely important for
a good representation of the system under analysis. Besides, there must be a very good
equivalence between the system under analysis and the conceptual model to guarantee great
consistency to the agent-based model and reliability from the simulation results.
Figure 2 presents a conceptual model to study pension funds governance. Streit
(2006) developed this model for regulatory governance analysis of sectors under regulation.
The conceptual model is generic and, consequently, it is useful to structure different
pension funds scenarios.
structural
level
External
context
parameter
External
context
parameter 2.
External
context
parameter N
System Domain
(ae level
Participant
agent 1
Participant
agent N
structural
level
Measures:
of the
model
Internal
context
variable 1
Internal
context
variable N
Figure 2 - Generic conceptual model to study pension funds governance.
Simulation along the time is the strategy to analyze the emergent phenomenon of
the model. The intentional level (action level), where the interactions among the agents
occur, is differentiated from the structural or contextual level. The structural level indicates
the contexts where the interactions happen, e.g., the circumstances that limit, amplify and
determine the interactions among the agents and with the environment. Moreover,
structural level is the level where the emergent phenomenon takes place. It is a higher level
comparing to the intentional level where the agents interact. The basic principle that guides
the model is that all interactions have an intention or a set of intentions. For a better
understanding, follows the main components of the generic conceptual model:
= Measures of the model: they are the results of the model that make possible the
study of the phenomenon for which the model is developed;
= External context parameters: indicate external aspects that may contextualize the
model. They are not influenced from the behavior of the model (unidirectional
arrow from the structural level to the individual level), but they can influence the
interactions among the agents who act in the intentional level of the model
(example: international indicators). The external context parameters define the
external environment of the system under analysis;
= Internal context variables: represent important external aspects. These variables
influence the interactions among the agents and are influenced by them. Thus,
during the simulations, the values of these variables are modified depending on the
interactions at the intentional level of the model. They express, in its totality,
relative external situations of the system under analysis in the environment;
= Government agent: it represents the government at the individual level of the model.
The government agent defines the regulation policies of the pension funds;
= Participant agents: they represent the agents who participate in a pension fund. The
participant agents are directly influenced by the regulations and situations that
impact the pension fund sector. The amount of “participant agents” in the model
will depend on the type of analysis and abstraction desired;
= Non-participant agents: they interact with other agents at the individual level, but
they do not participate in a pension fund. The non-participants agents are indirectly
influenced by the regulations of the sector and they can indirectly influence the
agents who regulate the sector.
The “internal context variables” and the “external context parameters” belong to the
structural level of the model (macro level).
2 A dynamic Asset and Liability Managemt (ALM) approach for pension funds
Pension funds need to produce a high-income return to correspond to actuarial
expectations and to pay different kind of benefits. Because of its long-term obligations, an
ALM model of a Pension Fund must consider a large planning horizon. ALM must control
the solvency of the fund by acceptable investments and contribution policies. The process
requires a great amount of information about the organization, its operations and market
performance. It comprises: (1) better understanding of the wealth of the organization by
evaluating balance sheet; (2) actions to control credit, liquidity and market risks (3)
statistical and mathematical methods to predict, forecast or foresee how the future should
be or define a finite number of scenarios to model uncertainty.
One of SD’s paradigms is that the structure determines behavior and events are
snapshots of that behavior. One step back from events is the idea of behavior patterns as
something that connects together a long series of events over time. They show sources of
pressure and imbalances that cause things to change. Pension funds have to decide
periodically how to allocate the investments over different asset classes and what the
contribution rate should be in order to fund its liabilities.
Risk and uncertainty are key features of most pension funds and need to be
understood to made rational decisions. A problem has many uncertainties and they are
materialized in various elements or factors in a risk analysis model as ALM. There are
basic principles that an ALM model concerns to:
= Deterministic modeling involves using a single “best guess” estimation of each
variable within a model to determine the models outcomes;
= Sensitivities determine how much that outcome might vary via what-if scenarios.
Every possible value that each variable could take is weighted by the probability of
its occurrence to achieve this. Each uncertain variable has a probability distribution
that needs to be considered in an ALM model;
= Within a risk analysis model, available data and expert opinions are the two sources
of information used to quantify the uncertainty.
Computer simulations, among others, give to the analyst a way to generate data or
optimize the model to give the parameters that will materialize the uncertainty. The analyst
must revise the data he has available and assure they are both reliable and as representative
of the true uncertainty as possible.
Many techniques try to fit theoretical distribution to observed data and to give the
dynamic model ways to foresee or forecast the possible results via estimators and
probabilities. To do this, many authors has a common sense that each variable is correlated
with, or a function of, another variable within the model. System dynamics gives a way to
explore causation between variables and feedback loops that are responsible for problems
in a considered context. As stated by Sterman (2000, pg.141), “correlation among variables
reflect the past behavior of a system. Correlations do not represent the structure of the
system (...) correlations among variables will emerge from the behavior of the model when
you simulate it”. Professor Sterman also states “confusing correlation with causality can
lead to terrible misjudgments and policy errors”.
Engert and Lansdowne (1999), states that “risks are events or occurrences that
prevent a program from achieving its cost, schedule, or performance objectives. This way,
Chaim (2006) and Chaim (2007) applied system dynamics principles to ALM (Asset and
Liability Management) models, in the specific case of pension funds. The author did a
research with actuaries and financial managers of 20 Brazilian pension funds. Figure 3
shows the results materialized in a causal loop diagram that represents the complexity of a
benefit plan of a pension and that include population dynamics as a way to reduce pension
costs.
Salary Administrative
taxes
<withdrawal/ % +
termination ———B= Pension costs
Tale> .
Expected retum
- ‘ vt
+
Actuarial
interest rate
Plan’s
stiactivity, = contributions
- + + * ~
age of each
Present value of participant and "Autiusial
future their relatives goals
* contributions +
New participants Salary increases
Ng Present value of
future benefits Mosalty'ette
+
~ withdrawal’
ae termination
F 2 tad Long term
inflation
Estimated costs disability rate
ofbenefit’s plan retirement rate
Ting of
contnbuition i ©
€ “& Mathematical s
provisions 7
Liabilities
Assets ;
<Actuarial 2
goals>
+) Solvency of the
+ plan
Ww Liquidit
i iquidity
Investment return
Plan’s maturity
Figure 3: A broad causal loop diagram obtained by expert opinion
Source: Adapted from Chaim (2007).
Three rounds of Delphi technique gave conditions to structure this causal loop
diagram and to analyze causation between factors. These factors were obtained by many
declarations of actuaries and practices statements from financial managers. Among others,
there are three feedback loops that constitute the main hypothesis about the causes of
dynamics under investigation by the research in progress:
RI — Good Solvency: more attractive plans may attract more participants or more
sponsors that may generate more accumulation. This way, the solvency tends to get better
by the reduction of the estimated costs of the plan;
B1 — Credibility: more attractive plans may obtain more participants and then the
costs tend to be lower, because they share the staff of the plan and material resources;
B2 — Good Wealth: more attractive plans may attract more participants or more
sponsors that may generate more accumulation. This way, the solvency tends to get better
by the reduction of the estimated costs of the plan and, thus, enhancing the attractivity of
the plan.
To constrain the scope of the article, attractive plans will consider just credibility
factor in population models. These article will not consider the calculating of pension costs
and mathematical provisions as in Rodrigues (2004). The value of mathematical provisions
of benefits to be paid of a participant with age x is represented by the equation MPx =
PVFBx — PVFC and its value consider population factors and they will be determined by
the equation:
MP. = FCS[S,.1+CS)"™.,.. pe div" —(S,_,,.CN(%).d,,. {x <r}, where
MP = Mathematical provisions;
(PVFB = Present value of future benefits):
FCS = Capacity factor of salary. It reflects inflation.
CS = Salary enhancement;
S,.+CS)'™.= salary of one participant, projected to the retirement age r
r—x = Fora participant of age x, the time remaining between the ass
date and the retirement date (r)
,-. P<" = the probability of a participant of age x to be alive and active when
‘ssment
reaching the age x of retirement
dG, = factor of anticipated actuarial income related to the participant when
initiating the retirement
vy’ = discount factor considering the interval between ages r and x
(PVFC = Present value of future contributions):
S,.,, = All salaries between ages x and r
CN(%) = Taxes that represents the cost of the plan
G,,,.. = factor of an anticipated actuarial income, temporary, related to activity
period of the participant.
Actuarial literature does not consider subjective factors since like credibility in
ALM analysis. For example, the uncertain parameters identified by Rocha (2001) were
interest rates, administrative taxes, capacity factor of salaries and benefits and the rates of
salaries increase, all of them economical factors. Lifetime and demographical studies also
do not consider subjective factors.
Causal loops relations may represent the uncertainty and may predict the impact of
each of it in the system as a whole. Chaim (2006) noticed that the use of system dynamics
in combination with asset-liability management model (ALM) represents an opportunity to
amplify its capability to become risk oriented. Streit (2006) indicate the use of subjective
factors using agent based models. Thus, macroeconomics, biometrics and actuarial classes
of variables must holistically considerer the incorporation of risk factors, subjective factors
and constraints (shortfalls) into the model.
Retirement . _
decrement Disability
ma a
~ ; -_ ,
Population xm
weit NE
participants —_-——~"__ g ~
" } decrement
Mortality
decrement
Figure 3: Populational decrements causal loop diagram.
Because pension funds are typically a multi-decrement environment
(WINKLEVOSS, 1977, p. 10-22), the causal loop diagram of figure 3 shows the dynamics
of a benefit plan. Credibility influences new adhesions made by word of mouth and ad
campaigns (R1); many decrements since like mortality (B1), withdrawal (B2), disability
(B3) and retirement (B4) are the balancing way to reduce this population and thus the costs
of the benefit plan (WINKLEVOSS, 1977, p. 10-22). Follows details about each one:
RI — Credibility: means that people become more and more interested in adhering
to a benefit plan of a pension fund. It means more assets coming from the participants and
the organizations that are sponsors of the benefit plan. Credibility generates confidence that
tends to foster new adhesion of new participants;
BI - Mortality decrements: “among active employees prevents the attainment of a
retirement status and hence the receipt of a pension benefit, while mortality among
pensioners acts to terminate the payment of their pension benefit” (WINKLEVOSS, 1977,
p. 12);
B2 — Withdrawal decrements: this decrement is also called termination decrement
and like the mortality decrement, “prevents employees from attaining retirement age and
receiving benefit under the plan (...) there are a multitude of factors entering into the
determination of employee termination rates, but two factors consistently found to have
significant relationship are age and length of service. The older the employee and/or the
longer his period of service, the less likely it is that he will terminate employment”
(WINKLEVOSS, 1977, p. 15-16). Accordingly to Winklevoss (1977, p. 18), “disability
among active employees, like mortality and withdrawal, prevents qualification for a
retirement benefit and, in turn, lowers the cost of retirement”.
B3 — Disability decrements: “a typical disability benefit might provide an annual
pension, beginning after a waiting period, based on the employee’s benefits accrued to data,
or on his projected normal retirement benefit. When disability benefits are provided outside
the pension plan, it is common to continue crediting the disabled employee with service
until normal retirement, at which time the auxiliary plan’s benefits cease and the employee
begins receiving a normal pension” (WINKLEVOSS, 1977, p. 18-19);
B4 — Retirement decrement: “the retirement decrement among active employees
initiates the pension payments” (WIKLEVOSS, 1977, p. 21).
Figure 4 shows the stock and flow diagram to manage the population dynamics of a
pension fund. Credibility is a factor that influences new adhesions and used a lookup table
based on parameters obtained by expert opinions.
Aging ratio
| ee
Intensity of Expected population
adhesions aging of the plan
Retirement ratio
Disability ratio
Adhesions Aging index
Maintaned benefits ratio
A
Total participants
Adhesion ratio
O ep] Active Pensioners pO)
participants ; ‘
‘Rew pales Plan’s Maturity Cessation
credibility ratio Pengonee
ye Withdrawal Mortality
‘decrements zane
credibility
withdrawal ratio
Pensioners>
Mortality Mortality
ratio decrements
Figure 4: Population dynamics stock and flow diagram.
The figure assumes a pension fund with an expected credibility rate that influences
new adhesions. People who are active participants are exposed to mortality, disability,
withdrawal and retirement risks. A pensioner is exposed just to mortality risks. An expected
population-aging ratio uses historical data and calculates the aging index. This dynamic is
essential an ALM model estimate the total assets and the flow of liabilities, maintain a good
solvency and prevent against liquidity risks.
In a SD way, a lookup table aids to model credibility as a factor that influences
accumulation and liabilities. It may enhance or reduce the adhesions of new participants
over time. According to Edmonds (2003), in cases where the field of study is sufficiently
complex, it is impractical or even impossible to rely only on mathematical models.
Therefore, the construction of an agent-based model appears to be the most suitable way to
s the impact of the social-economic and political issues on the pension funds
participants and non-participants.
For the analyst uninitiated in risk analysis modeling, it’s difficult to find explicit
techniques that will produce an accurate model of the problem in hand. To fill that gap, this
article proposes the combination of SD, agent based modeling and fuzzy logic.
3 Agent model and fuzzy logic
One of the major concerns in the process of developing agent-based models is with
the nature of the agents themselves and the definition of their behavior, that is, how they
interact with other agents and with their environment (Edmonds, 1998). The agents
modeling at the intentional level will define the way they take decisions, their behavior and
attitudes during the simulation experiments. The author argues that the purpose of modeling
the agents is to reveal the emergent behavior of the system. In the literature, it is possible to
identify diverse types of agent frameworks that have been conceived for various types of
analyses.
The agent model used in the research was based on the BDI (beliefs-desires-
intentions) architecture. BDI has been used for the modeling of different types of agent
behavior, and adopted in numerous fields. BDI agent architecture was introduced by the
philosopher Michael Bratman (1999), who proposed a framework for understanding ways
of characterizing mental attitudes and rational actions in human beings, in terms of their
intentions. The principles of Bratman's work have been fundamental for the theoretical
formalization of computational agents with rational behavior, and for the development of
formal agent architectures.
In BDI, agents are described as a set of beliefs, desires and intentions. The agents’
decision-making process occurs during analysis of beliefs relative to their desires,
according to the precepts of this approach. Beliefs are items of information held by the
agent about himself and about the environment in which he is active. They correspond to
the informative component of the agent's status and may be subject to uncertainties and
errors. Desires, in turn, are objectives the agent adopts and attempts to achieve. In terms of
BDI architecture, an agent's desires are essentially the ‘options' or 'possibilities' available to
the agent (Wooldridge and Parsons, 1988). The theoretical model of the BDI architecture
also employs the concept of intentions, which represent courses of action chosen by the
agents to achieve their goals (desires). The agent's actions are organized into plans. In the
process of deliberation, after the selection of an intention, an agent's plan is chosen and
initiated. Thus, intentions correspond to the agent's plans under execution.
Since the relevant beliefs, desires and intentions of agents are of a subjective nature,
the specification of the agents in this research employed a fuzzy-extension BDI agent
model (Shen et al., 2004). The basic idea behind the use of the fuzzy extension for
modeling multi-agent systems is the specification and description of the agent behavior by
means of fuzzy rules. The inference of these rules can be understood as the mapping
between a set of inputs and a set of outputs. Thus, the inference of these rules during
simulation establishes the dynamic behavior of each agent in the system and, as a
consequence, the behavior of the system as a whole. The practical reasoning of the agent
consists of two principal activities (Shen et al., 2004; Schut et al, 2004): (i) deliberation,
where the agent decides what to do (which intention to carry out); and (ii) planning, which
is the decision of how to carry out the intention.
In order to simplify the model proposed, the agent's deliberation (what to do) and
planning (how to do it) processes have been combined into one process. In this case, the
agent's practical reasoning mechanism consists in choosing a pair <objective, plan> for
execution, that is, the intention the agent can adopt and the plan of action for carrying out
such intentions. This simplification was suggested in the work of Hsieh et al. (2004). The
figure 5 represents the internal model proposed for the agents and indicates its principal
components (Streit, 2006). These components can be described as:
= Perceptions: refers to the means by which the agent perceives the environment;
= Agent's status: refers to the agent's current set of beliefs about its environment and
by the intention it is currently pursuing;
= Database pair <objective,plan>: data structure storing the possible space state of an
agent's pair <objective,plan>;
= Database ‘Beliefs’: stores the agent's beliefs about its environment;
= Components ‘revises beliefs’ and ‘selects <objective,plan>’: they are components
that carry out the procedures for the selection of the agent's intentions and action
plans. These components constitute the agent's decision-making process, along with
the component ‘deliberation control’;
= Action: component that executes the actions for carrying out the current intention or
the new intention selected by means of the fuzzy logic;
= Action outlet: refers to the means by which the agent transmits messages to the
environment and to the other agents. It is the outlet for the outcome of the agent's
inference process.
revise beliefs je ------
select <objective, |.
plan>
Agent status
Intention
selection
Lee [see
Fuzzy-inference
system
Figura 5: Agent’s internal model.
As presented in figure 5, the process of carrying out the intentions is based on fuzzy
logic. This process is circumscribed by the component denominated ‘fuzzy-inference
system’. In this case, the fuzzy rules execute the agent's actions following the BDI
framework. The agent's beliefs are defined on the antecedent term of the fuzzy rules (IF
side), while the term relative to the agent's deliberation is found on the consequent side
(THEN side). The main definition step of the model i ociated with the selection of the
production rules to model the agents’ behavior. For instance, the fuzzy rule "IF inflation is
high AND inflation variation increases THEN exert moderate pressure for interest rate
reduction " indicates, for example, that there is an agent belief that inflation is high and,
also, there is a tendency towards increased inflation. Then, the agent deliberation will exert
a moderate pressure into the ‘monetary authority’ agent for an interest rate reduction. The
value resulting from the pressure will depend on the degree of truth of the input variables
‘inflation’ and ‘inflation variation’ to the fuzzy sets ‘high’ and ‘increases’, respectively.
The notion of a fuzzy set was introduced by Zadeh (1965 apud Rizzi et al., 2003, p.
365), in the decade of 60. The objective is to represent mathematically uncertainties and to
supply formal tools to deal with the inherent imprecision of many problems. The main idea
is the revision of the classical theory of the sets. The traditional way of representing
elements “ of aset A is through the characteristic function (Kasabov, 1998):
Hw 1 if “ is an element of set A, and
HW = 0. if “ is not an element of set 4,
that is, an object “ either belongs or does not belong to a given set. In fuzzy sets theory an
object can belong to a set partially. The degree of membership is defined through a
generalized characteristic function called membership function: A, ():U > lo 1" where
U is the universe and A is a subset of U . The values of the membership function are real
numbers in the interval lo 1 where 0 means that the object is not a member of the set and
1 means that it belongs entirely.
The fuzzy logic has been considered useful when the process (system under
analysis) is difficult to forecast or model using traditional methods (Mohammadian and
Kingham, 2004). This paradigm allows the modeling of complex systems by the use of
simple rules that are defined with linguistic variables and terms. The fuzzy logic is versatile
because it allows the modeling and manipulation of vague and inexact information
mathematically. This type of information is natural in the human language, as the
information supplied by the specialists (not mathematicians) (Amendola et al., 2004). This
feature, according to Berg et al. (2004), it is an important advantage, because it allows the
linguistic interpretability of the model results and the comparison to the specialists
knowledge. The use of fuzzy-inference mechanisms is an interesting option for modeling
the reasoning and behavior of the agents. It makes possible to describe the agents’
behaviors semantically using production rules (IF-THEN).
In addition to the work of Shen et al. (2004), other studies in the literature
demonstrate the advantages of using fuzzy logic in the development of agent models
(Bossomaier et al., 2005; Li et al, 2004; Hsieh et al, 2004; Shajari and Ghorbani, 2004).
Fuzzy logic has been employed in the agent decision-making process and in the definition
of agent behavior.
4 Combining SD and agent-based model
The main stage of the agent-based model definition in this study is the production
rules selection to model the agents’ behavior. The criteria that can be used to the production
rules delimitation is based on the variables used in the dynamic model and the agent-based
model.
The figure 6 presents the main components of the model and simulation techniques
discussed in this article.
External Context Parameters
Structural level
Ji Jt
Social-Economic and Political Model
(Agent-based Model)
Pension Fund
Agent
P. Non a (Dynamic Asset
articipant Non articipant
Participant Liability Model)
Intentional twat /
External Context Parameters
Structural level
Figura 6: Conceptual model for pension funds.
The information to model the behavior of the agent considers the integration of two
qualitative research methods: (i) content analysis research; and, (ii) in-depth interviews.
They can provide data to model the agents’ behavior by means of fuzzy logic rules and a
systematic collection and interpretation of data produced in textual form as well as
knowledge from experts.
4 Conclusions
In this paper, the authors have attempted to show the power of combining SD and
agent based modeling methods with fuzzy logic. Because they use aside these methods in
their doctorate thesis, they are convinced that it is a good way to model subjective factors
since like credibility and knows the importance of it in a risk analysis methodology to
pension funds.
By simplicity, this paper focuses on population dynamics for a pension fund but the
authors are considering other methods and techniques to better simulate the complexity of
pension funds systems considering their risks and uncertainties.
The research is multidisciplinary and interdisciplinary by nature and the article
presents part of the literature review.
The research is in progress. The authors identified the main actors and the
methodology to proceed the modeling recommendations identified on the literature review.
The software to be produced will consider ages, mortality, withdrawal and mortality rates,
assets, liabilities, investments and many other factors from the database of a important
Brazilian pension fund company.
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