Associative memory approach to modeling stock market trading patterns
The proposed research intends to use the ideas of stochastic Theory of Social Imitation (W. Weidlich, E. Calen and D. Shapiro, T. Vaga ), and of the associative memory approach to modeling the dynamical structure of polarization relationships (S. Levkov and A. Makarenko) for modeling the stock marke...
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Makarenko, A. Levkov, S. Solia, V. 2010-12-10T17:44:50Z 2010-12-10T17:44:50Z 2007 Associative memory approach to modeling stock market trading patterns / A. Makarenko, S. Levkov, V. Solia // Систем. дослідж. та інформ. технології. — 2007. — № 4. — С. 111-124. — Бібліогр.: 20 назв. — англ. 1681–6048 https://nasplib.isofts.kiev.ua/handle/123456789/14081 519.5 The proposed research intends to use the ideas of stochastic Theory of Social Imitation (W. Weidlich, E. Calen and D. Shapiro, T. Vaga ), and of the associative memory approach to modeling the dynamical structure of polarization relationships (S. Levkov and A. Makarenko) for modeling the stock market trading patterns. The method potentially will allow us to forecast the offer and demand dynamics of a particular security, and lead to modeling of the assets price behavior. Our approach is based on the attempt to utilize the principles of certain classes of neural networks to reveal and model the underlying structure of the real dynamical process. Also the models with internal structure of brokers are considered and results of computer experiments are discussed. Приведены результаты исследования, использующего идеи стохастической теории социальной имитации (W. Weidlich, E. Calen и D. Shapiro, T. Vaga) и ассоциативной памяти в моделировании динамической структуры отношений поляризации (С. Левков и A. Макаренко) на примере фондовой биржи. Метод потенциально позволяет предсказывать динамику спроса и предложения и моделировать динамику цен активов. Предложенный подход базируется на попытке использовать принципы некоторых классов нейронных сетей для моделирования основной структуры реального динамического процесса. Рассматриваются модели брокеров с внутренней структурой и результаты компьютерных экспериментов. Наведено результати дослідження, в якому використовуються ідеї стохастичної теорії соціальної імітації (W. Weidlich, E. Calen і D. Shapiro, T. Vaga) та асоціативної пам’яті у моделюванні динамічної структури відносин поляризації (С. Левков і О. Макаренко) на прикладі фондової біржи. Метод потенційно дозволяє передбачати динаміку попиту та пропозицій і моделювати динаміку цін активів. Запропонований підхід базується на спробі використання принципів деяких класів нейронних мереж для моделювання основної структури реального динамічного процесу. Розглянуто моделі брокерів із внутрішньою структурою та результати комп’ютерних експериментів. en Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України Методи оптимізації, оптимальне управління і теорія ігор Associative memory approach to modeling stock market trading patterns Подход на основе ассоциативной памяти к моделированию фондовой биржи Підхід на основі асоціативної пам’яті до моделювання фондової біржі Article published earlier |
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| title |
Associative memory approach to modeling stock market trading patterns |
| spellingShingle |
Associative memory approach to modeling stock market trading patterns Makarenko, A. Levkov, S. Solia, V. Методи оптимізації, оптимальне управління і теорія ігор |
| title_short |
Associative memory approach to modeling stock market trading patterns |
| title_full |
Associative memory approach to modeling stock market trading patterns |
| title_fullStr |
Associative memory approach to modeling stock market trading patterns |
| title_full_unstemmed |
Associative memory approach to modeling stock market trading patterns |
| title_sort |
associative memory approach to modeling stock market trading patterns |
| author |
Makarenko, A. Levkov, S. Solia, V. |
| author_facet |
Makarenko, A. Levkov, S. Solia, V. |
| topic |
Методи оптимізації, оптимальне управління і теорія ігор |
| topic_facet |
Методи оптимізації, оптимальне управління і теорія ігор |
| publishDate |
2007 |
| language |
English |
| publisher |
Навчально-науковий комплекс "Інститут прикладного системного аналізу" НТУУ "КПІ" МОН та НАН України |
| format |
Article |
| title_alt |
Подход на основе ассоциативной памяти к моделированию фондовой биржи Підхід на основі асоціативної пам’яті до моделювання фондової біржі |
| description |
The proposed research intends to use the ideas of stochastic Theory of Social Imitation (W. Weidlich, E. Calen and D. Shapiro, T. Vaga ), and of the associative memory approach to modeling the dynamical structure of polarization relationships (S. Levkov and A. Makarenko) for modeling the stock market trading patterns. The method potentially will allow us to forecast the offer and demand dynamics of a particular security, and lead to modeling of the assets price behavior. Our approach is based on the attempt to utilize the principles of certain classes of neural networks to reveal and model the underlying structure of the real dynamical process. Also the models with internal structure of brokers are considered and results of computer experiments are discussed.
Приведены результаты исследования, использующего идеи стохастической теории социальной имитации (W. Weidlich, E. Calen и D. Shapiro, T. Vaga) и ассоциативной памяти в моделировании динамической структуры отношений поляризации (С. Левков и A. Макаренко) на примере фондовой биржи. Метод потенциально позволяет предсказывать динамику спроса и предложения и моделировать динамику цен активов. Предложенный подход базируется на попытке использовать принципы некоторых классов нейронных сетей для моделирования основной структуры реального динамического процесса. Рассматриваются модели брокеров с внутренней структурой и результаты компьютерных экспериментов.
Наведено результати дослідження, в якому використовуються ідеї стохастичної теорії соціальної імітації (W. Weidlich, E. Calen і D. Shapiro, T. Vaga) та асоціативної пам’яті у моделюванні динамічної структури відносин поляризації (С. Левков і О. Макаренко) на прикладі фондової біржи. Метод потенційно дозволяє передбачати динаміку попиту та пропозицій і моделювати динаміку цін активів. Запропонований підхід базується на спробі використання принципів деяких класів нейронних мереж для моделювання основної структури реального динамічного процесу. Розглянуто моделі брокерів із внутрішньою структурою та результати комп’ютерних експериментів.
|
| issn |
1681–6048 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/14081 |
| citation_txt |
Associative memory approach to modeling stock market trading patterns / A. Makarenko, S. Levkov, V. Solia // Систем. дослідж. та інформ. технології. — 2007. — № 4. — С. 111-124. — Бібліогр.: 20 назв. — англ. |
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| fulltext |
A. Makarenko, S. Levkov, V. Solia, 2007
Системні дослідження та інформаційні технології, 2007, № 4 111
УДК 519.5
ASSOCIATIVE MEMORY APPROACH TO MODELING STOCK
MARKET TRADING PATTERNS
A. MAKARENKO, S. LEVKOV, V. SOLIA
The proposed research intends to use the ideas of stochastic Theory of Social Imita-
tion (W. Weidlich, E. Calen and D. Shapiro, T. Vaga ), and of the associative memo-
ry approach to modeling the dynamical structure of polarization relationships
(S. Levkov and A. Makarenko) for modeling the stock market trading patterns. The
method potentially will allow us to forecast the offer and demand dynamics of a par-
ticular security, and lead to modeling of the assets price behavior. Our approach is
based on the attempt to utilize the principles of certain classes of neural networks to
reveal and model the underlying structure of the real dynamical process. Also the
models with internal structure of brokers are considered and results of computer ex-
periments are discussed.
1. INTRODUCTION
Associative memory is one of the models used in Artificial Neural Networks
(ANN) — field of research which has enjoyed a rapid expansion and increasing
popularity among the financial analysts. This is a completely different from the
conventional algorithmic model form of computation. Neural network consists of
numerous elementary processors arranged in a network, each programmed to per-
form one identical simple processing task. Such technology allows ANN to simu-
late intelligence in pattern detection, association, and classification problem-
solving.
Finance and economic problems solved by ANN fall into three categories [1]
(1):
• Classification and prediction (analysis of bankruptcy, loan default, bond
rating);
• Function approximation (valuation of assets from actual data, risk man-
agement);
• Time series forecasting (prediction of stocks, bonds, and other trading as-
sets' prices).
It is generally recognized that Artificial Neural Systems (ANS) are most ef-
fectively applied to the problems of classification and clustering. The successful
applications of neural networks include business failure prediction [1], credit
scoring and credit performance forecasting, risk assessment of mortgage applica-
tion, bond rating, financial and economic forecasting. The idea here is to formu-
late the task of a particular forecast as a classification problem: given a set of
classes (for example, bankrupt and non-bankrupt, well-performing and poorly
performing firms), and a set of input data vectors, the task is to assign each input
data vector to one of the classes. The input vector components are usually the dif-
ferent financial ratios (like net sales / total assets for bankruptcy prediction) or
A. Makarenko, S. Levkov, V. Solia
ISSN 1681–6048 System Research & Information Technologies, 2007, № 4 112
different parameters (like confidence, growth, anticipated gains for the stock price
performance prediction). The numerous ANNs solving classification problems
differ basically in the neural network configuration, learning algorithms, and
number, choice, and coding of input vector components. Usually, it is hard to
compare different authors’ approaches to a particular problem, since they optim-
ize the network structure and input parameters in accordance with the training and
test sets of historical financial data they have chosen, and this choice is pretty
much arbitrary. Nevertheless, whatever ANN approach is implemented, it is gen-
erally performing better than the conventional forecasting techniques (discrimi-
nant analysis, regression methods, statistical techniques, etc.).
Among the other potential applications which merit further research, are:
portfolio selection and diversification, simulation of market behavior, index con-
struction, identification of explanatory economic factors, and other problems re-
quiring massive parallel processing, fast retrieval of large amounts of information,
and the ability to recognize patterns based on experience. Especially interesting
financial problem, where an ANN is useful, is pricing and hedging derivative se-
curities [2]. Here, the task of the neural network is to uncover (approximate) a
value function describing the relationship between inputs and outputs. It can be
done due to the universal approximation property of the learning network. More-
over, certain classes of ANN can approximate arbitrary well any continuous func-
tion on a compact domain, which means that there is always a choice for the net-
work parameters that is better than any other possible choice [2].
Another promising and already quite developed area of ANN applications is
time series forecasting. Time series are a special form of data where past values in
the series may influence future values, depending on the presence of underlying
deterministic forces [3]. A significant portion of real-time series is generated by
nonlinear processes and besides, is highly contaminated by noise. Therefore, the
task of ANN is to uncover the “true” relationship between variables using its
learning ability. The idea here is to break the time series into the past and future
sets. Then, the network is trained and learns on the past set of data and tested on
the future set to see how well its forecast fits into the real data.
While a good deal of ANN applications has focused on the prediction of
stock price dynamics, it has been noted that only moderate success has been
achieved to date [4].
The reason for that, to our perception, is that one of the advantages of ANN -
their ability to model non-linear processes with a few (if any) a priori assump-
tions about the nature of the generating process - becomes a disadvantage here.
Forecasting (if ever possible) the time series behavior with a strong stochastic
component without modeling the underlying dynamical system may well result in
a failure or just a random success.
As an attempt to model such an underlying dynamics, many publications
have appeared recently regarding the applications of non-linear dynamics and
chaos theory to the prediction of stock market behavior [5]. Most of the works in
this field are either trying to apply directly the well-known facts from the dynami-
cal chaos theory to the financial systems, or investigate the existence of dynami-
cal chaos and its parameters in the financial time series.
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 113
As an example of applying the ANN related ideas (associative memory, in
particular) to model the underlying dynamical structure of the financial markets,
the work of Tonis Vaga can be cited [6]. This work is based on the theory of so-
cial imitation [7], and polarization phenomena in society [8], that go back to the
famous Ising model — the model for ferromagnetism that describe the behavior
of simple magnets. The Theory of Social Imitation extends it to the phenomenon
of polarization of opinions in a variety of social groups. The assumption here is
that individuals in a group behave similar to the molecules in a bar of iron. Under
some conditions, the individuals’ thinking becomes polarized, which means that
they will act as a crowd and individual rational thinking will be replaced by a col-
lective “group think” [8]. Such transitions from disorder to order and otherwise,
share the same macroscopic characteristics, whether we deal with physical, bio-
logical, chemical, sociological, or financial system.
Unlike chaos theory, which seeks to forecast the stock prices time series in a
deterministic (although dynamically chaotic) sense, the market hypothesis of Va-
ga based on the Ising model, give a method to analyze the transition from random
walk behavior to periods of coherent price trends, and periods of chaotic fluctua-
tions of market as a whole. However, the Theory of Social Imitation and Vaga’s
approaches give only a theoretical basis and are not intended for the forecasting of
the actual trading dynamics or price movements, since it is essentially based on
stationary state analysis of potential wells of distribution functions.
On the other hand, the attempts to construct a neural network-based mathe-
matical model describing the underlying individualized dynamics of the social
polarization phenomena have appeared recently in works of S. Levkov and A.
Makarenko [9, 10, 11]. In those works, the analog of Ising model in the form of
Hopfield associative memory network [12], was used to make the strategic fore-
cast of geopolitical structures’ (GPS) evolution and formation of blocks. The idea
of the approach is to present the GPS as a network of elements characterized by
the state variables describing the generalized power of a country and interconnec-
tion matrices describing the relationships between them. The reconstruction of
interconnection matrices is based on historical patterns of inter-relations using a
Hopfield Network Algorithm. The problem was considered of modeling the for-
mation of bipolar and tripolar block structures depending on different initial con-
ditions and parameters of interconnections. The key element is to construct the
evolution law based upon the appropriate definition of energy of interconnections
and of field of influence.
The proposed research intends to use the above mentioned ideas of stochas-
tic Theory of Social Imitation (W. Weidlich, E. Calen and D. Shapiro, T. Vaga ),
and of the associative memory approach to modeling the dynamical structure of
polarization relationships (S. Levkov and A. Makarenko) for modeling the stock
market trading patterns. The method potentially will allow us to forecast the offer
and demand dynamics of a particular security, and lead to modeling of the assets'
price behavior. We would like to emphasize here, that in contrast to the existing
ANN models, where the real process is considered as a “black box”, and ANN is
trained on the sets of input and output data to simulate the nonlinear relationship
between them without actually revealing the nature and structure of the prototype
A. Makarenko, S. Levkov, V. Solia
ISSN 1681–6048 System Research & Information Technologies, 2007, № 4 114
process, our approach is based on the attempt to utilize the principles of the cer-
tain classes of neural networks to reveal and model the underlying structure of the
real dynamical process.
2. JUSTIFICATION OF APPROACH.
2.1. Can the market be predicted?
There is still a big controversy regarding this matter. Some of the authors think
that the market is non-predictable. Their popular expression is “You can’t beat the
market”. Indeed, evidences and academic studies of professionally managed port-
folios have shown that professional investors as a group not only fail to perform
better than amateurs, but that it is even difficult to find individual portfolios
which have achieved performance significantly better than neutral. The others are
even more pessimistic and think that institutional investors will, over the long
term, underperforms the market [13]. Nevertheless, the majority of institutional
investors believe that they can outperform, and therefore predict, the market; oth-
erwise they wouldn’t step into it. Besides, numerous financial analysts consider
that making market forecasts does make sense (most of the endnote articles are
devoted to forecasting one or other aspect of the market process).
The reason that forecasting methods make sometimes more, sometimes less
correct predictions, lies, to our opinion, in the Coherent Market Hypothesis of
T. Vaga [6]. According to it, the stock market has four major states: random-walk
state, coherent bull market, coherent bear market, and chaotic market. The state of
the market is controlled by the investor sentiment and the prevailing bias in eco-
nomic fundamentals. The random-walk state, or efficient market, is characterized
by low risk and, consequently, low reward. This is a period when investor senti-
ment is not conducive to “group think’ or crowd behavior. When economic fun-
damentals are positive (bullish) and investor sentiment is conducive to crowd be-
havior, the coherent bull market emerges. This is the safest, most rewarding state
of the market. The coherent bear market is also characterized by low risk and high
reward and is a result of the combination of negative (bearish) economic funda-
mentals and crowd behavior. The last major market state identified by Vaga, is a
chaotic market. During this period, a high degree of polarization exists among the
investors, but the economic fundamentals are neither positive nor negative, which
results in the most dangerous market state with high risk and low reward.
Not going into further details of Vaga’s analysis, we can conclude that an
opportunity to forecast the stock market behavior arises during the periods of co-
herent behavior. A similar approach can be applied also to a particular stock. The
most interesting (yet more complex) problem in this case would be forecasting the
transition periods from one market state to another.
2.2. Conventional theories of market forecasting.
Traditionally, two approaches to asset valuation and price prediction have been
used - the “firm-foundation theory” and the “castle-in-the-air theory” [14]. The
firm-foundation theorists believe that each investment instrument has its “intrinsic
value” that depends on the present conditions and future prospects of the firm.
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 115
Consequently, an opportunity to make money arises when the market price falls
below or rises above this firm foundation of intrinsic value. In contrast, the castle-
in-the-air theorists concentrate on people’s psychology. Analyzing how the crowd
of investors is likely to behave in the future and how they tend to build their
hopes into castles in the air under favorable market conditions, supposedly allows
estimating what investment situations are most susceptible to public castle build-
ing and buy before the crowd.
Accordingly to these two views on the stock market, there are two opposite
investing techniques - fundamental and technical analysis. Fundamental analysts
believe the market to be 90% logical and 10% psychological. Therefore, they care
little about the particular pattern of the past price movement, but rather seek to
determine the proper value of the security. It is done by analyzing growth pros-
pects, dividends payout, level of interest rates, and the degree of risk. Once the
“true” value of the company is determined, the fundamentalist can start his game,
since to his beliefs, the market will eventually reflect accurately the security’s real
worth. There are numerous examples when this theory fails and makes wrong
predictions. Apparently, this approach underestimates the role of market and its
participants in the mechanism of establishing the actual asset price.
In contrast, the technical analysis suggests that all the information about
earnings, dividends, and the future performance of a company is already reflected
in the company’s past market prices. It presumes that the price chart and the trad-
ing volume are the only information needed for correct prediction. Essentially, the
main technical analyst’s task is to anticipate how the other investors will behave.
Therefore, the true technical analyst doesn’t even care to know what business or
industry a company is in, as long as he can study its stock chart. There are also
plenty of cases when this theory fails. This approach obviously neglects the role
of information about firm fundamentals in the price formation and focuses mostly
on market effects.
Evidently, those theories are two extremes. The price generically depends on
the firm fundamentals but is determined on the market through the trading
process. Therefore, the adequate models of the price dynamics should inevitably
consider the market participants, their relationship, and their behavior.
2.3. The role of market structure and market relationships in price forma-
tion.
The financial theorists and practitioners are mostly uniform in determining who
the market participants are. Basically, they divide them into the following catego-
ries [15]:
• Market makers or Specialists;
• Brokers;
• Uninformed traders (or Nice traders [16], or Noise traders [17]);
• Informed traders (or News traders [16], or Insiders [17]).
Some of the classifications, instead of informed and uninformed traders, in-
clude traders possessing special information, “liquidity-motivated” traders who
have no special information but merely want to convert securities into cash or
cash into securities, and traders acting on information which they believe has not
yet fully discounted in the market price but which in fact has [18]. Another ap-
A. Makarenko, S. Levkov, V. Solia
ISSN 1681–6048 System Research & Information Technologies, 2007, № 4 116
proach breaks them down into differentially informed traders and liquidity traders
[19].
Trading takes place through the market makers and must pass through a bro-
ker. Such structure does not allow public to participate directly in the trading.
Therefore, in order to understand the market mechanism, first, it is necessary to
understand the relationship between market makers on one side and brokers
representing their anonymous clients on the other. Moreover, as Jack Traynor
(more known under the pseudonym Walter Bagehot) wrote in his famous and
widely cited article “The Only Game in Town”, “the market maker is a key to the
stock market game”. Technically, his role is to provide liquidity by stepping in
and transacting whenever equal and opposite orders fail to arrive in the market at
the same time. For this purpose, the market maker transacts with anyone who
comes to the market. But still, any market maker has an ultimate goal of making a
profit from his transactions. He always loses to informed traders; therefore the
gains from the transactions with uninformed and liquidity-motivated traders must
exceed these losses. Thus, the market maker can be thought as a channel through
which money from uninformed and liquidity-motivated traders flow to insiders,
since those who get information make the profit from the market makers, and the
latter earn from the other traders who don’t have it.
Another aspect that makes the market even more complicated is the broker -
market maker relationship. Since the market maker’s spread between bid and
asked price mainly depends on the difference between his losses to informed trad-
ers and gains from the others, he will readily reduce it if the broker reveals that
his client trades, for example, just for liquidity purposes. Better execution of or-
ders means more clients for the broker. On the other hand, in order to make such
relationship work, the broker also has to reveal when his client is informed, which
will definitely lead to the poorer execution of his order. Thus, the broker faces the
dilemma: whether to tell the specialist when his client is a news trader and per-
haps, lose him, or conceal this fact and get poorer execution for all the other
clients’ orders. Since uninformed and liquidity-motivated traders are in absolute
majority in the stock market, the broker has an incentive to reveal the informed
traders. However, if informed traders were always identified, they would be
forced out of the market; because the market maker would set such a spread that
the advantage an informed trader has might disappear. Nevertheless, news traders
are in the stock market, which means that they are not always correctly identified
either because the broker makes mistakes, or because the broker chooses rando-
mizing strategy when sharing the information with the market maker.
This picture of the stock market, being simplified, shows nevertheless, that
the way the market participants interact with each other, their beliefs and disbe-
liefs, credibility and trustworthiness have considerable impact on the price forma-
tion.
2.4. Possibilities for modeling.
The above analysis shows that a possibility of forecasting the market behavior
may exist at least for some periods of market dynamics and for particular securi-
ties. The adequate models of the price dynamics should inevitably include the
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 117
market participants, their relationship, and their behavior. The interaction of mar-
ket participants, their beliefs and credibility have significant influence on the
market trends. The combination of methods of stochastic theory of social imita-
tion (W. Weidlich, E. Calen and D. Shapiro, T. Vaga), and of the associative
memory approach to modeling the dynamical structure of polarization relation-
ships (S. Levkov and A. Makarenko) represent a solid foundation for developing
the model of the stock market trading patterns that would allow to forecast the
offer and demand dynamics of a particular security, and lead to modeling of the
assets' price behavior.
3. THE MODELING CONCEPT
3.1. General ideas
We present here briefly the core idea of the approach and the rough draft of the
model that we are going to develop in the research. The proposed model does not
pretend to be full and is intended only to demonstrate the basic ideas presented
here.
Assumptions.
In order to make easier understanding of the method and to simplify the ini-
tial formulas, we consider the idealized market of one security. The trade consists
of discrete steps, at which the actual transactions take place. Within each step we
identify the sub steps, which describe the dynamic bidding and asking or deci-
sion-making processes for every individual. The market consists of N homoge-
neous participants (in future developments the homogeneous assumption obvious-
ly should be removed).
With every trader we associate the state variable ,2,1,0{ ±±=∈Ssi
}, iM± , where is represents the number of shares that trader i is planning to
buy (if 0>is ) or to sell (if 0<is ), and iM is the maximum allowed trading vo-
lume, which represents the number of shares trader isi able to buy.
With every pair of traders i and j we associate the variable R∈ijc — the
integral value of reputation that trader j has from the point of view of trader i .
This value measures the degree of how well informed; trader j is in the eyes of
the trader i . The large positive values of ijc mean that, in the opinion of trader i ,
trader j is an informed (news, insider) trader, the values close to zero can mean
that the trader j is an uninformed (noise, nice) or liquidity trader, while the nega-
tive values mean that the trader j is either insider who trades against the informa-
tion he has in order to hide himself, or a trader who is likely to be wrong in his
judgment. The reputation variables ijc form a matrix
NjiijcC ,...,1,}{ == . (1)
that we call the matrix of reputation. The approach ijc valuation will be discussed
later at the end of this section.
A. Makarenko, S. Levkov, V. Solia
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As one of the basic characteristics of the system we introduce the concept of
a vector field of influence
0,:}{ ,,1 === ∑= ii
j j
j
ijiNii c
M
s
cffF (2)
where if means the integral influence of opinions of all other participants on i
trader. The intuition behind this formula is the following. The ratio
j
j
M
s
represents the trading intentions of participant j at the current step. It shows the
number of shares trader j is planning to buy or sell as a percentage of what his
actual buying or selling power is. The product
j
j
ij M
s
c × is the information about
intentions of trader j filtered through the matrix of reputation. Thus, the sum (2)
represents all the available to trader i information about the actions of other par-
ticipants, and since it is filtered through the matrix of reputation, it is meaningful
and trustworthy to him. We would like to note here, that all the other information,
trader i might have, is already incorporated in his initial intentions to buy or sell
is .
Obviously, the best strategy for rational individual will be to adjust his own
initial intentions to the filtered information about others. Speaking formally, we
say that every participant is associated with the information utility function,
which he is trying to maximize during the decision-making process. It is done by
correlating the trading decision of individual i with the corresponding value of
the field of influence if .
Thus, we may formulate the evolution equation describing the trading dy-
namics:
−><−
<>+
=+
.otherwise
,)(and0)(if,1
,)(and0)(if,1
)1(
i
iiii
iiii
i
s
Mtstfs
Mtstfs
ts (3)
The initial conditions for this dynamic equation are the intentions of each in-
dividual to buy or sell at the beginning of the trading step. They are formed under
the influence of the sources outside the system, and represent the trader’s forecast
of how well the particular stock will be doing.
Given the initial conditions for is and known values of influence matrix, we
may calculate the dynamics of the trading patterns. Such dynamics is expected to
be beneficial for each trader, since it leads to the maximal utilization of the fil-
tered, and therefore useful, information available to him.
Obviously, the system consists of protagonists with different and frequently
antagonistic goals. Thus, the actions beneficial for a particular participant do not
necessarily benefit the others. Moreover, each trader acts from his own interests
and generally, if somebody wins, someone loses. However, all these egoistic indi-
viduals comprise the system we consider. Therefore, from the system point of
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 119
view the question is, whether the defined above dynamics of every trader leads to
a meaningful evolution of the whole system, or is this just a disordered, chaotic
motion? The answer can be found using the analogy with the physical systems.
As the variable summarizing the evolution of the system, we introduce the
concept of energy E , which characterizes the impact all the traders have had on
each other in making their buying/selling decisions:
∑−=
i
ii sfE .
Thus, at any given point in time, energy E characterizes the state of the
market. Naturally, we are interested in the evolution of the trading patterns lead-
ing to a state that has the property of stability. By analogy with the physical sys-
tems, we will call the state of the system stable if the energy E has a local mini-
mum in this point. As we will see, the system will tend to minimize its energy
during the evolution process. To show this, we will first formulate and prove the
following statement.
Statement 1. Under the law of evolution (3) the system evolves to a local
minimum of energy E .
After energy reaches the local minimum, due to (A1) any change of the state
of the system will increase the energy, which is impossible because of (A2). Thus,
)()1( tsts ii =+ i∀ , and the system will retain its stable state until some external
forces are applied. Such stable state can be thought as an equilibrium, at which
trading takes place and shares change their hands. It simply means that all the par-
ticipants have reached their decisions having maximized their own information
utility functions. Since we are assuming that all the external information the par-
ticipants might have is represented by their initial intentions, trading occurs. Thus,
maximization of individuals’ information utility functions leads to the minimum
of energy of the system and, therefore, to its coordinated movement during the
decision-making step.
The next trading step begins with the new initial conditions, which contain
the new information traders have been able to obtain.
The reputation matrix in the described above model remains invariable dur-
ing the bidding/asking or decision-making steps. Obviously, it should change at
each trading step, since traders analyze their own performance as well as the per-
formance of other participants and market as a whole. Therefore, each individual
might assign different coefficients to the corresponding elements of the matrix of
reputation, which will be enforced at the next trading step.
Thus, the reputation matrix plays one of the major roles in the proposed
model, and the applicability of the model depends, to a great extent, on the cor-
rectness and accuracy of the reputation coefficients. The numeric values for the
entries of the matrix of reputation are not readily available. However, one of the
advantages of the given approach is that it uses already proved and experimental-
ly tested algorithms for the identification of the matrix C via the prior observa-
tions of the trading patterns. This algorithm has the form of the well-known rule
from the pattern recognition theory of associative memory models [12]. Its brief
idea can be outlined as follows.
A. Makarenko, S. Levkov, V. Solia
ISSN 1681–6048 System Research & Information Technologies, 2007, № 4 120
Suppose we have recorded information about trading patterns kZ ,
Kk ,,1= , where }{ ik sZ = at the time moment k , K is the number of obser-
vations, Ni ,,1= , N — number of traders. Then the matrix of reputation C
can be evaluated as
∑ =×==
k
ii
j
jk
i
ik
ijij c
M
s
M
s
ccC 0,},{ . (4)
3.2. Accounting the internal structures of market participants
The next step in development of proposed models is to account the internal struc-
ture of agents (we named such agents as ‘intellectual’).
Let us consider the idealized market as the collection of N intellectual
agents. We will consider the process with discrete time steps. Each agent should
to do decision (change of state) at each time step in dependence of all agents’
states [20].
Agent’s state is described by the variable },,2,1,0{)( ii MStS ±±±=∈ ,
which corresponds to the amount of the recourse (information, materials and so
on), which may be gain ( 0)(if <tSi ) or collect ( 0)(if >tSi ) by i individual
(agent). Here Mi is the maximal volume of its resource (its potential). Interac-
tion of individuals in organization is described by influence matrix }{ ijcC = ,
Nj ,,1= , ]1,0[∈ijc where ijc — influence coefficient of j individual on
i . The influence matrix C may reflect the authority power in organization. In sim-
plest model we take 0=ijC , Ni ,,1= .
So the collection ( )}{)},({)( R
lj
R
l
R CtStQ = , Nji ,,1, = represents the real
state at moment t. Let us consider also ( )}{)},({)( i
lj
i
l
i CtStQ = , Nlji ,,1,, = as
ideal pattern of situation from the i agent point of view. Then we can calculate
the difference between real and ideal patterns of situation:
)()()( tQtQtD Ri
i −= . (5)
We suppose that the dynamics of i agent depends on the difference )(tDi
and on the mean influence field by other agents. We accept the influence field
)}({)( tgtG i= , Ni ,,1= as:
∑
=
=
N
j j
R
jR
iji M
tS
Ctg
1
)(
)( . (6)
The term
j
R
j
M
tS )(
j
R
j
M
tS )(
in (6) corresponds to the activity of j agent at the
moment t . The term
j
R
jR
ij M
tS
C
)(
corresponds to activity with reputation accounting.
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 121
In general case the dynamical law for agent takes the form (F some law
for agent’s reaction, named frequently activation function):
))(()1( tvFtS i
R
i =+ , (7)
where the argument )(tvi may takes the form:
а) Multiplicative
)())(()( tgtDtv iii α= , (8)
where for example )())(( tDk
i
ietD −=α . In simplest evident variant we may take:
∑
=
−=
N
j
R
j
i
ji tStStD
1
)()()( ; (9)
b) additive ))(()()( tDftgtv iiii += , where ))(( tDf ii — some influence
function. The simplest example is:
∑
=
=
N
j j
i
j
R
jR
iji M
SS
CtDf
1
)(
))(( . (10)
In this model vector )(tvi represent the understanding by i agent on the
tendencies in market: If 0)( >tvi , then the tendency is to increase the recourse, if
0)( ≈tvi , then the stability is the main tendency, if 0)( <tvi , then the ten-
dency is to reduce the resources.
One of the most usable forms of activation function F in such type models
are:
−>>−
<>+
=+
,othervise0
,)(and
)(
)(if1)(
,)(and
)(
)(if1)(
)1( i
R
i
i
R
i
i
R
i
i
R
i
i
R
i
i
R
i
R
i MtS
M
StG
tvtS
MtS
M
StG
tvtS
tS (11)
where
N
tg
tG
N
i
i∑
== 1
2 )(
)( . (12)
Remark that very interesting development of proposed models consist in in-
troduction time dependence of connections by some dynamical laws. Of course
the models described here correspond to the constant bonds.
A. Makarenko, S. Levkov, V. Solia
ISSN 1681–6048 System Research & Information Technologies, 2007, № 4 122
4. RESEARCH TASKS AND PROBLEMS TO BE SOLVED
Proposed approach allows developing the software and trying to understand some
properties of market. Here we describe some examples of computer experiments
with the models (5)–(12) which accounting the internal structure of brokers and
non-constant in time reputation of brokers.
The horizontal axe corresponds to the steps of trading. The vertical axe
represents the intentions of different traders. The left picture correspond to stabi-
lization of intentions of traders. The right-side picture corresponds to the case of
market with changeable bonds (reputations) during trading.
The right picture illustrates the possibilities of oscillations of the market. The
oscillations are intrinsic for market with asymmetrically informed brokers. More-
over the market with mostly asymmetrically informed brokers may have chaotic
behavior. Other very interesting phenomenon is the possibilities of sudden
changes of stable trading patterns of market evolution in the case of variable repu-
tation of traders. It may correspond to real phenomena in the market. Also it may
correlate with phenomena of punctuated equilibrium in biology.
Of course till now our computational investigations are model with artificial
date and further investigations will be interesting. But just now some prospective
issues may be discussed.
First of all proposed internal representation may be considered as some cor-
relate to ontology of market participant. Also it may be interesting for considering
classical problem of reputation. At second the approach reminiscent usual multi-
agent approach. The description of trader remember agent with special representa-
tion of the internal and external worlds by network structure. Also the prospec-
tive feature in the approach is the associative memory in proposed models.
Fig. 1. Modeling the market trading
Associative memory approach to modeling stock market trading patterns
Системні дослідження та інформаційні технології, 2007, № 4 123
5. CONCLUSION
Thus in proposed paper we consider the approach for market modeling which im-
plement some properties of real market. The main distinctive features are the ac-
counting of internal properties of traders. As the authors envisage, the modeling
principles, described in section 3 can lead to the formulation and solution of the
following problems:
1. Development of models of trading patterns for the specific markets.
2. Enhancement of the models of trading patterns with price formation mod-
els and developing the price forecast methods.
3. Numerical simulation of specific markets.
4. Establishing of the asset price dynamics through the offer/demand-price
relationship.
Partially Supported by State Fund of Fundamental Investigations Grant
№ Ф25/539–2007.
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Received 11.06.2007
From the Editorial Board: the article corresponds completely to submitted
manuscript.
Dear Serjeza, Happy New Year with best regard from I and Kolja. Big privet
vsem Ire,Yure and Tanya Barzilovich.
Your Alla/
ASSOCIATIVE MEMORY APPROACH TO MODELING STOCK MARKET TRADING PATTERNS
A. Makarenko, S. Levkov, V. Solia
1. Introduction
2. Justification of approach.
2.1. Can the market be predicted?
2.2. Conventional theories of market forecasting.
2.3. The role of market structure and market relationships in price formation.
2.4. Possibilities for modeling.
3. The modeling concept
3.1. General ideas
3.2. Accounting the internal structures of market participants
4. Research tasks and problems to be solved
5. Conclusion
Fig. 1. Modeling the market trading
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