Cybernetic Approach to Portfolio Management

Cybernetic approach to portfolio
management
Marchev, Jr., A., A. Marchev

Contents1. Introduction
2. Epistemology
3. Semantics
• Investment
• Cybernetic
4. Portfolio as a controlled system
5. Portfolio management
• Design of control system
• Design of subsystems
6. Self-perfection in the process of portfolio management
7. Models of investors
8. Concept of competition of models
9. Historical Simulation
• Dealing with data imperfections
• Simulation results
10. Conclusions
• Causes for some peculiar results
• Heuristic restructuring
• Some points for discussion
6.9.2015 г. Marchev, Jr., Marchev 2

Introduction
• Cybernetic approach is based on the scientific achievements of
the “cousin” fields of:
– Cybernetics
– General systems theory
– Control theory
– Information theory
– Operations research
• Universal language among the various domains of knowledge
• Concept for automatized and autonomous decision making
• Studies on cybernetic approach for portfolio management are
not common but they do exist (e.g. Duncan, Pasik-Duncan,
1987; Lian, Li, 2010; Hanson, Westman, 2002; Durtschi,
Skinner, S. Warnick, 2009; Costa, Maiali, Pinto, 2009; Skaf,
Boyd, 2010; Dombrovsky, Lashenko, 2003; Lim, Zhou, 2001;
Primbs, Barmish, Miller, Yuji, 2009).

Epistemology
• Inductive reasoning - no predefined research hypothesis other than
the intuitively known:
– there are some models which would perform better than others
– every model could be dissected into procedural blocks that correspond to
stages of implementation of the model.
• Systematic approach:
– The portfolio is observed as a system of similar sub-portfolios.
– Each model of investor is observed as a system which could be further
dissected into subsystems.
• Exhaustive and complete data set - experimenting with all usable
data
• Empirism - current research is focused on proving, disproving and
discovering new facts and relations entirely based on the existing
real-world data.

Epistemology (continued)
• Heuristics - after every model has been tested against real-world data
and later disassembled into separate blocks, the experiments move
to combining the blocks of different models into new unstudied
models.
• Self-organization (through directed selection) - all modifications
(sets of parameter values) of all models are tested against each other
on a unified track of data. Using threshold criteria, the best
modifications are selected and are used for generating a new set of
modifications and models.
• Complexity - the unrestricted (but regulated) financial market
environment is a complex system encompassing many
interdependent active subsystems and their various non-linear
interactions.

Epistemology (continued)
• Discrete time - the studied phenomena as discrete-time and based
on the evident available data.
• Interdisciplinary nature - such research does not belong to a single
domain of knowledge but rather represents a cross-fertilization of
ideas, ranging between financial economics in the social sciences
field and automatic control engineering, while drawing upon
necessary premises in the field of evolutional science and
systematization of the human thought.

Semantics
• Investing - process of consciously sacrificing own resources in the
pursuit of future reward or goal. None of the future outcomes is
guaranteed to offset the undertaken restriction of investor’s
degrees of freedom (Alexander et al, 1993, p. 840; Marchev, 2012a).
• Investor - entity (physical or legal), purposefully using financial (and
other) resources for investment and pursuing future rewards. It is
assumed (although not exhaustively proven) that such entity acts
rationally as a real Homo Economicus (Mill, 1836).
• Securities - are investment opportunities (investment instruments,
investment vehicles, investment assets), traded freely on a
transparent market on which information that is relevant enough is
publicly transmitted (Luenberger, 1997, p. 40).

Semantics (continued)
• Portfolio - combination of securities owned by a given investor. All
entities possess (knowingly or not) / (purposefully or not) a
portfolio of some sort. The focus is on portfolios that combine
securities traded on regulated financial markets and knowingly
owned by investors (Jones, 1994, p. 7; Fischer et al., 1995, p.12).
• Reasoning of the portfolio - improve the conditions of the
investment process by obtaining such properties (values of
significant variables) of the combined securities that are not
obtainable by any single security.
• Portfolio properties - most often (but not the only) considered
significant variables are risk and return. A certain configuration of
risk and return is only possible within a given combination of
securities. Improving risk and return conditions through portfolio
management is diversification (Marchev, 2012a).

Control system
Portfolio
Investor
1. Goals
2. Observed influences from the environment
(market factors)
3. Controlling influences
4. Unobserved influences from the
environment
5. Insignificant variables (?)
6. Significant variables
7. Feedback
2
5
3
4
7
6
1

Control using computer model
Portfolio
Investor
Computer model
1. Goals
2. Observed influences from the
environment (market factors)
environment
7. Feedback
8. Task for the computer model
9. Proposed controlled influences
2
5
8
3
4
29
7
6
7
1

Computer model with adjustment
Portfolio
Investor
Computer model
Self-perfecting
subsystem
1. Goals
2. Observed influences from the environment
(market factors)
environment
7. Feedback
8. Task for the computer model
9. Proposed controlled influences
10. Adjusting the internal structure and/or the
values of the variables of the computer
model
Important remark: all information channels are assumed
to be noisy and with delays.
2
5
8
3
4
2
10
9
7
6
7
1

Portfolio management as a Black box
Портфейл
Инвеститор
Еталонен модел
Блок за настройка
1. Goals
2
5
8
3
4
2
10
9
7
6
7
1
Complex system for managing of
investment portfolio

• Controlling system - investor with a defined set of desired states for
the portfolio. The investor transforms the output information from
the portfolio and the information about the desired states of the
portfolio into control input – a market order (Bodie et al., 1996, p.
858), (Marchev, Marchev, 2010b; Marchev et al, 2012b).
• Hierarchy – the controlling system is composed of subsystems of
lower levels
• Controlled system - investment portfolio (portfolio). It is an artificially
created and dynamically changing investment combination of a
structured set of named, mutually interconnected securities forming
a whole unity. Every investment portfolio has self-similarity features
i.e. the whole portfolio may be viewed as an investment security.

• Environment - the investment market is a complex system that is constantly set in
motion by many interdependent active subsystems (individuals acting on their own
free will) and the various non-linear interactions among them.
• Subsystem Security (as subdivision of the controlled system) – may be observed as
a portfolio of a single position with weight 1.00 (also “single portfolio”, “primitive
portfolio”)
• Element of the controlled system - unit of named security, which cannot be further
dissected within the research – i.e. a share of an issue of shares, traded on the
market.
• State of the portfolio system - a state space defined by the set of significant
variables, 〈S, T, I, G〉 where the behavior of the observed portfolio is the set of
consecutive states S, a set of sub-trajectories T, an initial state I, and a goal state G.
• Law of control - investor’s apriori stated strategy for portfolio management,
targeted at achieving the desired goals by observing the controlled system and by
accordingly ruling the controlling influences.

State of the portfolio system

Behavior of the portfolio system

The portfolio displays basic systemic features such as:
• Unity – the portfolio is observed and evaluated as a whole
unity (intact entity).
• Dissectability – every portfolio may be analyzed as a portfolio
of multiple portfolios, each consisting of multiple other
portfolios. Such dissection may continue until a portfolio is
reached which consists of only one element.
• Emergence – a portfolio as a whole has characteristics apart
from its subsystems. The effect of diversification is explained as
an emergent feature of a portfolio.
• Interconnectivity – relations among the portfolio’s subsystems
are defined by the existing interdependences between the real
economic agents that have issued the securities.

Portfolio as a controlled system
The numerical representation of a portfolio system requires that a portfolio
consists of k+1 positions, each with respective weights, where k is the total
number of positions traded on the market. For unwanted positions the
invested sum is set to 0. The uninvested sum is assumed to be a cash
position c(t). The sum of all weights equals 1.00. The numerical
representation of a portfolio is a k+1-dimensional vector of weights
summing to 1.00.

• The portfolio system is characterized by three
sets of variables:
A. Input variables
B. Internal variables.
C. Significant output variables.

Input variables
• Control input from the controlling Investor system: vector U(t), consisting of
k number of ordered correcting values. Each of the values corrects (is
summed with) the corresponding value of the current structure of the
portfolio. If the sign of a given correcting value is negative, the control
influence is to sell certain amount of the corresponding security. (2)
• Disturbances from the environment are mainly securities prices, in vector
P(t), consisting of k ordered market prices.

Internal variables
• Quantitative structure of the portfolio (vector Q(t)), measured in integer
number of owned unites of every security. If the number is negative, then a
short position is taken.

Internal variables
• Market valued structure (vector M(t)) consists of the market value for every
position in the portfolio. M(t) is computed by multiplying the market prices
for all securities (vector P(t)) with the current portfolio structure.

Significant output variables
• Market value of the portfolio as a sum of the market values of all the
positions.

• Weight structure of the portfolio – vector of relative weights for each
position, summing to 1.00.

• Real return – relative change of the market value compared to
moment (t-1)

• Cash position is a plug variable, computed as the difference between the
market value at moment (t-1) and sum of all positions in the market value
at moment (t).

Portfolio management
• The process of portfolio management could be analyzed in
several phases, ordered within a control cycle.
• Each phase is represented by a subsystem in the structure of
the controlling system Investor.
• The proposed structural design of a portfolio controlling system
aims at providing a general and universal solution to all
investment problems.
• In addition to being a process that is complex and dynamic in
nature, the investment portfolio management needs to
implement a controlling system of “requisite variety” following
Ashby’s Law (Ashby, 1958).

Structural design of the controller
CODER
PROCESSOR / TRANSFORMER
DECODER

• Setting goals - goal is a desired state (configuration) of the
significant variables. The task is comparing the current state
with the desired one. Very suitable for the task is the Sortino
ratio or its modification, because it is naturally goal oriented,
(Fabozzi et al, 2007).
• Feedback - Receiving, Collecting, Systemizing information on
the behavior and the structure of the portfolio.
• Observed external factors - Receiving, Collecting, Systemizing
information about the environment – market conditions and
constraints, obtainable investment opportunities, observed
external factors that influence the portfolio.

Structural design of subsystem “A.Goals processor”
AB. Linguistic stated
goals
AA. Objective
variables
AC. Selection
limitations
АD. Criteria for pre-
selection
CD
AE. Desired state/ area/
trajectory
АF. Current state/
area/ trajectory
BA
AG. Comparator
(-)
GH
DC
CC
Investment
goals
AH. Measures for
success
EA

Structural design of subsystem “B.Portfolio
information processor”
BA. Current state/ area/
trajectory
АF
HBBB. Portfolio
structure
BC. Statistical analysis
of the portfolio
Information
from the
portfolio

Structural design of subsystem “C.Environment
information processor”
CA. Securities
CC. Factors
influencing the
securities
CB. Market
conditions
CD. Filter
АD
CE. Pre-selected
securities
CI. Real
limitations
CH. Market
friction
DACF. Data-base
processor
CG. Mutual
funds
DB
GC
GE
GB
АC
Information
from the
environment

• Predictor - Forecasting/estimating the expected values
significant variables of the obtainable investment opportunities
and the external factors.
• Solution generation - process of defining and estimating the
portfolio’s feasible states as combinations of multiple primitive
portfolios.
• Using a reference (computer) model - computerized simulation
model for experimenting and evaluating the generated
solutions.
• Solution selector - making decision and selecting a portfolio
structure. Only the optimal solutions among all the feasible
ones are considered. There is a need for using multi-criteria
optimization and enforcing the principle of requisite addition.

Structural design of subsystem
“D.Estimator/predictor”
DB. Statistical analysis
of the factors
DC. Objective
variables
ЕADD. Estimation
of the factors
DA. Statistical analysis
of the data from the
securities
CF
CG
DE. Forecasting of
objective variables
АA
ЕA

Structural design of subsystem “E.Solution
generator”
EB. Data input to
the computer
model
EA. Combining the
securities, based on
expected values of their
features
DE
DD
ED. Set of optimal
solutions
GA
EC. Proposed
solutions from the
computer model
F F
AG

“G.Solution selector”
GB. Market friction
factors
GH. Criteria for
selection
GF. Decision
matrix
GA. Quantifier
(discretization,
validity, integrity)
ED
CH
GF. Selection of
solution (portfolio
structure)
АH
HA
GC. Limitations
CI
GD. Filter
GЕ. Mutual funds
CG

Матрица на алтернативите

• Translator/communicator of the controlling influences - the
controlling influences are administered, which also entails
realization of the solution. After the comparison between the
portfolio’s desired and current structure, the differences are
translated into market orders. Several real limitations would
interfere the realization of the decision, making it sub-optimal:
– Discretization, dissectability, availability of an issue of a given security – the
numerical problem becomes a whole number optimization problem.
– Delay of the reaction of the system, including the time for executing an
order, as well the time for meeting the conditions of the order.
– Market friction is the cumulative effect on the free trade from brokerages,
the inflation rate of the economy, taxes on capital gains and/or
dividends/interests, etc.

“H.Translator/communicator”
HB. Current portfolio
structure
HC. Comparator (-)
HA. Desired portfolio
structure
GF
BC HD. Translating the
difference into stock
market orders
HE. Defining the
type of each order
HF. Submitting the
orders
HG. Residual
deviations in the
orders
Partly
realized
orders

Real time control
• The Controlling system receives, processes and transmits
the required information for adequate time relative to the
observed changes in the environment and the controlled
system (i.e. relative to the frequency of the data)
• A control cycle is shorter than the shortest period of time
to register significant changes for the control system.
• The system’s sensibility to change of various intensity is
directly connected with the chosen frequency of studying
the system
• The minimal step for reassessing the portfolio is equal to
the minimum discretization step
• Within the current research the relevant BSE data is
considered to be daily data (not at all high-frequency
trading)

Self-perfection in the process of portfolio management
• Self-learning - process of adjusting the internal variables of the controlling
system by some sort of internal algorithm or a procedure, so that the significant
outcomes from the controlled system improve (approach the goals) while the
system is functioning.
• Self-organization - process of rearranging and reformatting the internal
structure (subsystems and connections among them) of the controlling system
by some sort of algorithm or a procedure, so that the significant outcomes from
the controlled system improve (approach the goals) (Marchev, Motzev, 1983).
• Automatization - minimization of human intervention in the process of portfolio
management, accomplished mostly by a computerized controlling system.
• Automation - very essence of cybernetics and control theory and it greatly aides
the processes of self-learning and self-organization (namely the “self-” part).
The use of automated portfolio management corresponds to the dynamically
changing investment environment (which means relatively short time for
decision available)

Self-perfection in the process of portfolio management
• The self-learning properties of the controlling system is
implemented through the self-perfecting subsystem in
the controlling system (see fig. 1):
– It represents the most complex version of the controlling
system Investor.
– It transforms all available information flows into purposefully-
administered (goal-oriented) adaptation adjustments toward
perfecting the reference model and thus the whole controlling
system.

Model of investor
Model of investor is an artificial abstract system
simulating the behavior of an imaginary investor
following a certain initially defined investment
strategy.
Includes:
• Principle model of an investor as a controlling sytem
• Block for investment strategy testing
• Set of simulated or historical data
• Computer model of the investment strategy

Classification of models of investor by phase of
development of the theory
• Preceding (intuitive, Naive)
• Classical
• Postmodern
• Vanguard (in process of development)
• Combinatory (by combining blocks)
• Selected

Concept for competition of models of investors

• All of the “models of investors” (whether known and new) should be back-
tested on the unified competition data track.
• Such competition track consists of complete time series of all possible
securities.
• The back-testing is done for every data-point (historical trading day) with
all possibilities (all securities available for trading on that day), using all
state spaces (all possible values of all parameters).
• The direct result of such systematic approach would be a ranking list of
the most successful (according to given criteria) portfolio “investors”
which then could be selected by a given treshold.
• Therefore, from a general perspective the overall concept encompasses in
fact a multi-stage selection procedure.

• Essence - The research focuses on a competition of models of investors,
based on historical data.
• Initial assumption - Every modification of every known approach to the
construction and management of portfolios may be represented by a
model of investor.
• Empirical data - The concept of unified competition track is introduced
mainly because of the real data imperfections.
• Incremental advance - Every model of investor is tested on each data
point with the full variety of modifications (all combinations of the feasible
values of all parameters). There is a minimal incremental step varying from
one day to one month. The historical data window, which is used for
estimation, reflects the period of previous data that the model uses –
from one month to five years. With each advance to the next data point,
the window “slides” forward as well. The horizon of prediction (between
one day and one year) also slides forward.

• Selection - In the course of the competition, the best modifications of
models are chosen by threshold selection. It should be noted that is that
instead of selecting the best one, the top several models are selected. This
is an implementation of the principle of inconclusive decision. It also
suggests that the procedure may be infinite (ergo not fitting the definition
of an algorithm).
• Dissection - Each of the selected modifications is observed as composed of
standardized blocks corresponding to the phases of portfolio
management.
• Heuristic restructuring - The dissected non-equivalent blocks from
different modifications are then assembled together to reconstruct new
(combinatory) models after being checked for compatibility.
• Iteration - The new combinatory models are competed on the data track
again.

• General objective - Automated (to some extent)
generation of new better models (concepts,
approaches, theories) for the construction and
management of investment portfolios.

0.6
0.8
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1.6
1.8
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133
136

Historical simulation
• Objective of the experiments - The objective is to conduct а series of
experiments of historical simulation for evaluating the return and the risk-
weighted return of various models of the process of portfolio management
(models of investors).
• Empirical data used in the research - daily closing prices of all investment
instruments traded on the Bulgarian stock exchange (BSE) for the period
between 28 November 1997 and 30 April 2011
• The main challenge with the data is the missing data due to the poor
trading activity especially in the early years of BSE’s existence. The missing
data has at least three serious implications:
– there are price time series which do not have enough data points to conduct
any reasonable analysis;
– in almost all price time series missing data imputation is required for further
analysis;
– in the initial trading sessions there are relatively large periods of trading
inactivity.

КОМПЮТЪРИЗИРАНА СИМУЛАЦИОННА СРЕДА ЗА СРАВНИТЕЛЕН
ЕМПИРИЧЕН АНАЛИЗ НА МОДЕЛИ ЗА УПРАВЛЕНИЕ НА
ИНВЕСТИЦИОННИ ПОРТФЕЙЛИ
Фаза за предварителна подготовка на масиви и
променливи
0. Предварително зареждане на информационните
масиви и задаване на начални стойности на
параметрите.
Фаза за подготовка на симулационната среда
1. Предварително подготовка и изчисляване на
стойностите на променливите, използвани от модела
за текущия цикъл.
2. Генериране на възможни решения.
3. Избор на решение за структура на портфейла.
Фаза за историческа симулация
4. Историческа симулация.
5. Проверка за край на алгоритъма.
Фаза за заключителни операции
6. Изчисляване на критериите за оценка на модела.
7. Допълнителна обработка и представяне на
резултатите от моделирането в удобен за анализ вид.

• List of the models of investors in the research

• Criterion for comparing the results - risk adjusted return for the whole
period of the research computed using Sharpe ratio, modified to compare
the realized return with the inflation rate for the period.

• Main varied parameter - investment horizon (L),
which shows the frequency of reconsidering the
portfolio on trading days, given that:
– the initial invested sum is 10000 BGN (~5000 EU);
– there is no new capital inflow, nor capital outflow;
– the initial capital is invested on the first date of the period
and is reinvested in full every time the portfolio is
reconsidered.

Формиране на използваната
емпирична база

Недостатъци на данните
• Основното предизвикателство, свързано с анализа на данни от
БФБ са липсващите стойности, поради невисоката активност на
търгуване, особено в началните години от започване на
търговията. Липсващите данни имат поне три сериозни
последствия:
– съществуват динамични редове, при които реалните данни (наблюдения) са
толкова малко, че не може да се проведе никакъв смислен анализ;
– в почти всички динамични редове е необходимо допълване на данни, за
провеждане на по-нататъшен целесъобразен анализ
– между началните периоди на търгуване има относително големи паузи от
нетърговски дни.
• За преодоляването на тези предизвикателства са предприемат
три прийома:
– обоснован избор на инвестиционните инструменти, включени в изследването;
– изключване на краевите ефекти, т. е. определен брой от най-ранните наблюдения;
– допълване на динамичните редове.6.9.2015 г. Marchev, Jr., Marchev 60

Избор на ИИ в изследването

Изключване на краевите ефекти в данните
•за първите 42 календарни дни от началото на борсовата
търговия (т.е. периода от 27.11.1997 до 06.01.1998) има общо 4
търговски дни на БФБ
•изключване на най-ранните данни за определен период от
време
•правило за изключване: всички първоначални месеци, с по-
малко от 20 търговски дни в месеца
•за начална е определена 01.01.1998, (първото наблюдение е на
07.01.1998)

Извадка на включените в изследването ИИ
• Забележка: Диаметрите на кръговете кореспондират точно на броя от ИИ от
съответните съвкупности в първичната база6.9.2015 г. Marchev, Jr., Marchev 64

Причини за липсващи данни
• инвестиционният инструмент не е бил допуснат до търгуване
или е спрян от търгуване;
• бил е допуснат, но не е имало сделки;
• бил е допуснат, имало (или нямало) е сделки, но липсват
сведения за това;
• ценната книга е търгувана за определен период, прекратена
е търговията й като данните за този период на са достъпни по
настоящем.

Допълване на данните
• За допълване на липсващите стойности е
използван метода „Последна наблюдавана
стойност” (Last value carried forward imputation
– LVCF)*
* Лазаров Д., “Оценка на липсващите стойности при финансови
динамични редове”, VSIM 2/2010, ISSN 1314-0582
( ) ( 1)i iP t P t 

Основен недостатък

ИИ след допълването, подредени по
общ брой стойности

ИИ, подредени по процент от покритие с данни
спрямо целия сеответен период на търгуване

Дневни доходности след LVPF

Дневни доходности и дисперсия след
LVPF

Markowitz
TobinSingle
Asset
Naive
Random
MSSP

Results and conclusion
(risk-weighted return)
09.06.2014 73Marchev, Jr. Marchev

Симулационни експерименти с
Модел на Марковиц

ЗАЩО?!?
• Може би заради метода на попълване на
липсващите данни?
• Доходност за периода край 2001 – края 2002 г.
– Формопласт АД – Кърджали (294%)
– Хидравлични елементи и системи АД (1979%)
– Алфа Ууд България АД (3200%)
• Доходностите и за трите са изчисление върху две
реални наблюдения, разделени от дълъг период
от липсващи данни.

Методи за допълване на данните
Реални данни LVPF
Линейна интерполация Средна от познатите стойности

Промяна на метода за попълване на
липсващи данни

Съпоставка на резултатите от markowitz.l1 при метод на
попълване на данни LVPF и при Линейна интерполация
0 500 1000 1500 2000 2500 3000
10
2
10
4
10
6
10
8
10
10
10
12
10
14
markowitz.L1 (LVPF)
markowitz.L1 (lin.interp)

Heuristic restructuring

Съпоставка на моделите по критерия средно време
в секунди необходимо за един цикъл на модела
0
5
10
15
20
25
30
35
asset naive rand markowitz tobin single mssp

Брой ИИ включени в портфейла по периоди
при различни модели на инвеститори
* Забележка: данните за single се припокриват с данните за markowitz и tobin

References
[1] Marchev, Jr., A., A. Marchev, “Cybernetic approach to selecting models for simulation
and management of investment portfolios (a general concept)”, 2010 IEEE
International Conference On Systems, Man And Cybernetics October 10-13, 2010,
Istanbul, Turkey
[2] The MathWorks, Inc., Simulink ®, 1994-2011,
http://www.mathworks.com/products/simulink/
[3] Milev, M. N., "Application of MATLAB for modeling and evaluation of financial
derivatives", Eudaimonia production Ltd., Sofia, 2012, ISBN 978-954-92924-2-8
[4] Duncan; T. E., B. Pasik-Duncan; Adaptive control of some continuous time portfolio
and consumption models, 26th IEEE Conference on Decision and Control, Dec. 1987,
Vol. 26, pp. 1657 – 1659
[5] Lian, K. Y., C. C. Li, "A Fuzzy Decision Maker for Portfolio Problems", IEEE International
Conference on Systems, Man, and Cybernetics: SMC 2010, 10-13 October 2010,
Istanbul, Turkey
[6] Georgieva P., I. Popchev. Cardinality Problem in Portfolio Selection. - M. Tomassini et
al. (Eds.): ICANNGA’2013, LNCS 7824, pp. 208–217, Springer-Verlag Berlin Heidelberg
2013
[7] Hanson, F.B.; J. J. Westman, Optimal consumption and portfolio control for jump-
diffusion stock process with log-normal jumps, Proceedings of the American Control
Conference, 2002, Volume 5, pp. 4256 – 4261, ISSN : 0743-1619

References (continued)
[8] Duncan, T.E.; B. Pasik-Duncan, L. Stettner, Parameter continuity of the ergodic cost for
a growth optimal portfolio with proportional transaction costs, 47th IEEE Conference
on Decision and Control, CDC 2008, 9-11 Dec. 2008, pp. 4275 – 4279, ISSN 0191-2216
[9] Durtschi, B., M. Skinner, S. Warnick, Portfolio optimization as a learning platform for
control education and research, American Control Conference, ACC '09, 10-12 June
2009, pp. 3781 – 3786, ISSN : 0743-1619
[10] Costa, O.L.V., A. C. Maiali, A. de C Pinto, Sampled control for mean-variance
hedging in a jump diffusion financial market, Proceedings of the 48th IEEE Conference
on Decision and Control, held jointly with the 2009 28th Chinese Control Conference,
CDC/CCC 2009, 15-18 Dec. 2009, pp. 3656 – 3661, ISSN : 0191-2216
[11] Skaf, J.; S. P. Boyd, Design of Affine Controllers via Convex Optimization, IEEE
Transactions on Automatic Control, Nov. 2010, Vol. 55 , 11, pp. 2476 – 2487
[12] Dombrovsky, V.V.; E.A. Lashenko, Dynamic model of active portfolio
management with stochastic volatility in incomplete market, SICE 2003 Annual
Conference 4-6 Aug. 2003, Vol. 1, pp. 516 – 521, ISBN: 0-7803-8352-4
[13] Lim, A.E.B.; X. Y. Zhou, Mean-variance portfolio selection via LQ optimal contro,
Proceedings of the 40th IEEE Conference on Decision and Control, Dec. 2001, Volume
5, pp. 4553 – 4558, ISBN: 0-7803-7061-9
[14] Primbs, J. A.; B. R. Barmish, D. E. Miller, Y. Yuji, On stock market trading and
portfolio optimization: A control systems perspective, American Control Conference,
2009. 10-12 June 2009, ISSN : 0743-1619

About the authorsassist. prof. Angel Marchev, Jr. PhD has graduated in finance at the
University for National and World Economy as a merit student.
He later finished master degree in Corporate finance at the
Burgas Free University. He persued a career as a Bank analystist
but found it is too formalistic and not enough challenging. Angel
is a PhD in applications of computer simulations in business.
Marchev Jr. Is a forth generation lecturer and it was only natural to
choose such career path. He is currently teaching at the UNWE
and BFU on „Stock markets and operatons”, „Computer
simulation”, „Fundamentals of management”
His scientific interests include (the list is far from exhaustive):
• cybernetics
• computer simulation, forecasting, quantitative methods in
management
• portfolio management, financial markets
• simulation and gaming
• self-organization, evolutionary algorithms, multi-stage selection
procedures, genetic algorithms, neural networks, fuzzy logic,
chaos theory
angel.marchev@basaga.org
+359888444062

About the authors
prof. Angel Marchev, Ph.D. has graduated with a golden medal
award as automation control engineer at the Technical
University of Sofia. Later he worked closely with A. Ivahnenko,
one of the originators of the concept of Self-organization.
Prof. Marchev is one of the pioneers of implementing cybernetics
and system theory in the fields of business management in
Bulgaria. Over the last 40 years he has published more than
two hundred papers on various topics in the field. He
considers as his life-time achievement the implementation of
Multi-stage selection procedures for wide range of business
challenges such as system identification, forecasting, modeling
economic and business systems among others.
He teaches courses such as “Simulation and gaming in
management”, “Business games”, “Computer simulation” and
“Financial modeling in management”, „Fundamentals of
Management I: Cybernetics and systems theory” at the
University for National and World Economy and Burgas Free
University among several others business schools and collages.
E-mail: angel_marchev@yahoo.co.uk

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