cybernetic approach to portfolio management

Cybernetic approach to portfolio management

Marchev, Jr., A., A. Marchev

Contents1. Introduction2. Epistemology3. Semantics

• Investment• Cybernetic

4. Portfolio as a controlled system5. Portfolio management

• Design of control system• Design of subsystems

6. Self-perfection in the process of portfolio management7. Models of investors8. Concept of competition of models9. Historical Simulation

• Dealing with data imperfections• Simulation results

10. Conclusions• Causes for some peculiar results• Heuristic restructuring• Some points for discussion2.05.2023 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).

2.05.2023 г. Marchev, Jr., Marchev 3

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. Goals2. Observed influences from the environment

(market factors)3. Controlling influences4. Unobserved influences from the

environment5. Insignificant variables (?)6. Significant variables7. Feedback

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Control using computer model

Portfolio

Investor

Computer model

1. Goals2. Observed influences from the

environment (market factors)3. Controlling influences4. Unobserved influences from the

environment5. Insignificant variables (?)6. Significant variables7. Feedback8. Task for the computer model9. Proposed controlled influences

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Computer model with adjustment

Portfolio

Investor

Computer model

Self-perfecting subsystem

1. Goals2. Observed influences from the environment

(market factors)3. Controlling influences4. Unobserved influences from the

environment5. Insignificant variables (?)6. Significant variables7. Feedback8. Task for the computer model9. Proposed controlled influences10. 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.

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Portfolio management as a Black box

Портфейл

Инвеститор

Еталонен модел

Блок за настройка

1. Goals6. Significant variables

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Complex system for managing of investment portfolio


Semantics (continued)• 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.


Semantics (continued)• 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


Semantics (continued)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 systemThe 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.


Portfolio as a controlled system

• The portfolio system is characterized by three sets of variables:

A. Input variablesB. Internal variables.C. Significant output variables.


Portfolio as a controlled system


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.


Significant output variables• Weight structure of the portfolio – vector of relative weights for each

position, summing to 1.00.


Significant output variables• Real return – relative change of the market value compared to

moment (t-1)


Significant output variables• 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


CODE

R

PROCESSOR / TRANSFORMER

DECO

DER

Structural design of the controller• 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

Structural design of the controller• 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

Structural design of subsystem “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. LimitationsCI

GD. Filter

GЕ. Mutual fundsCG

Матрица на алтернативите


Structural design of the controller• 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.


Structural design of subsystem “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.


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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 ПОРТФЕЙЛИФаза за предварителна подготовка на масиви и променливи0. Предварително зареждане на информационните

масиви и задаване на начални стойности на параметрите.

Фаза за подготовка на симулационната среда1. 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 операции6. Изчисляване на критериите за оценка на модела.7. Допълнителна обработка и представяне на

резултатите от моделирането в удобен за анализ вид.


Historical simulation• List of the models of investors in the research


Historical simulation• 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.


Historical simulation• 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.2.05.2023 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 база2.05.2023 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 LVPFЛинейна 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

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markowitz.L1 (LVPF)markowitz.L1 (lin.interp)


Heuristic restructuring


Съпоставка на моделите по критерия средно време в секунди необходимо за един цикъл на модела


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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 tobin2.05.2023 г. Marchev, Jr., Marchev 84

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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

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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

[email protected]+359888444062


mailto:[email protected]

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: [email protected]

mailto:[email protected]

cybernetic approach to portfolio management

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