In the next papers we

a) explore the application of statistics and  stochastic differential calculi ,   in macro-economics, micro-economics, insurance  and finance.

b) attempt a more elegant and concise representation of the formulae of actuarial mathematics (insurance) through standard formulations of stochastic processes. And through this a rational decision to the problem of which investments in pensions are better.

c) It is attempted to bridge some how the gap between academic techniques of statistics and forecasting with empirical techniques of financial  technical analysis in capital markets.

d) we give some applications of portfolio theory and stochastic dynamics,  worked out with data of the Greek capital markets.

e) we give estimations of liquidity that protect the investors in futures (derivatives) from the risk of bankruptcy.

 5) The impact of the convergence of the Greek economy to EMI in the Stockmarket: Bayes, nested estimation of the stock trends

By Dr.C.Kyritsis .Archives of Economic History  v. X, no1-2 ,(1999) pp 41-52.

(The same paper as word document)

Comments and Interpretation:

The paper discusses the consequences of the perspective of participation of Greece in the European Monetary Unification in the Greek Society and the Athens Stock Market. It makes use of a discrete time (time-series) simulation model for the Athens Stock-Market right after the Greek currency devaluation. Unlike the usual simulation models this model  is not  of stationary trend. The idea of non-stationary models came from empirical technical analysis curried out with massive computations of simulation for the Athens Stock Market of the magazine « Χρήμα και Αγορά ». In such simulations, that the random variables are normal, the forecasting of the regression path and its volatility gives practically all the information.

 6) Stochastic refinement of an optimal investment model of organizations by Jorgensen-Kort. By Dr.C.Kyritsis and P.Sharkey .Proceedings of the  Conference HERMCA 98 at the University of Economics in Athens v 1, pp 413-419. (1997-1998).

Comments and Interpretation:

This is a paper that gives a general method to render optimal control models in Economics to Stochastic Optimal Control Models. It is made use of  ITO’s stochastic differential equations (continuous time simulation).

7) An insurance  econometric asset valuation model of the National Technical University of Athens. By Dr. C. Kyritsis  and Prof. Kiochos (University of Pireas).

Proceedings of the 11th Greek Conference of Statistics held at the  University of Crete , in Chania 5-9 June  1998.(1996-1998).

(The same paper as word document)

 Comments and Interpretation:

This is the publication summary of a study for the insurance of the Buildings and Equipment of national Technical University. Due to lack of sufficient easily analyzable accounting data, it is used  statistical econometrics. To the final estimation is  attempted a continuous time best fit simulation with ITO’s stochastic differential equations of constant growth.

8) Stochastic refinement of Pecorinos optimal inflation-rate model.

By Dr.C.Kyritsis and Prof. P.Kiochos (European Research Studies Journal .University of Pireas v 1, issue 4 1998 pp 77-84).

 (The same paper as word document)

 Comments and Interpretation:

The model of Pecorino asserts that the optimal for society is have non-zero inflation rate and specifies how much. The idea is that inflation is an indication of a growing economy.

The model of Pecorino is deterministic and is rendered to stochastic with the general method used also in the paper 7) . It is made use of  ITO’s stochastic differential equations (continuous time simulation).

9) How to compare bank savings and insurance pensions.

By Dr. C.Kyritsis and Prof. P. Kiochos (University of Pireas Volume of essays in Honor of Professor  M. Raphael 2000, pp 347-372) , (written 1996-1999).

 (The same paper as word document)

Comments and Interpretation:

The results of this paper are of interest to the Insurance policies dealers and all that want to invest in insurance pensions. The comparison is slightly in favor of Bank savings. It is carried out statistical forecasting at the end of the paper.

10) The risks of bankruptcy in insurance companies and stochastic stability co-author P.Kiochos (University of Piraeus Volume of essays in Honor of Professor  M. Raphael 2000, pp 399-408) written 1998.

 (The same paper as word document)

Comments and Interpretation:

This is paper that applies results of stochastic stability of continuous time simulation models to the investment of insurance companies. Unlike the traditional analysis of the risks of bankruptcy through discriminant analysis ,we apply here stochastic differential equations of constant growth models.

11) Optimal Portfolio from stocks of the Index FTSE/20 in the Athens StockMatket and the Period 1997-1999 .Co-author A. Kiochos  ( Archives of Economic History 1999  v XII no, 1-2 pp 147-156).

(The same paper as word document)

 Comments and Interpretation:

This is a classical optimal portfolio selection method that is applied to the Athens Stock Market. The mathematical techniques belong to non-linear programming of operations research.

12) "Estimation of required liquidity for investment position  in futures of the Athens derivatives exchange market." by Costas Kyritsis Published in  "Essays in honor of the  professor Nikolaou" of the University of Piraeus 2001 pp 729-735, Greece.

(Te same paper as word document)

Comments and Interpretation:

In this paper we discuss the risk of mark-to-market  loss of positions with leverage, in futures. We make the usual assumptions of Lognormal distribution and geometric Brownian motion for the underlying  as in the Black-Scholes options pricing model. With these assumptions  we estimate tables of  required liquidity for futures on FTSE-20 and FTSE-40 in the Athens Derivative Exchange Market, during the year 2000.

13) The relation of Fuzzy subsets, Postean and Boolean lattices .The λ-rainbow lattices . The transfinite real Fuzzy subsets.(First version 1992)

By Dr Costas Kyritsis. . Technical University of Crete ,Proceedings of the VII  Congress of Sigef 2000 pp 763-774.(1992) .

 (The same paper as word document)

Comments and Interpretation:

In this paper is proved a kind of equivalence between Boolean (2-valued logic), Postean  (3-valued logic), and Fuzzy-subsets (Fuzzy logic) lattices.

As Fuzzy logic is considered an extension of 3-valued logic we introduce an extension of the Postean lattices based on an order type λ, as spectrum of logical valuations, under the name λ-rainbow lattices. We introduce, also, a kind of arithmetical representation of the λ-Fuzzy subsets lattices, in a manner much the same that an geometric line segment  is an interval of real numbers. We make use of the transfinite real numbers of A. Glayzal that later became known and rediscovered by J.H.Conway as surreal numbers.

14) "Time-series Simulation of the income of insurance-brokers ,in Greece(1997)

co-author: P.Kiochos. Published in the volume B "Essays in honour of the late professor

D. Kodosakis" of the University of Pireas 2001, Greece pp 533-540.(The same paper as word document)

15) "Estimation of maximum average loss for investment position in futures of the Athens derivatives exchange market." co-author: A. Kiohos Archives of Economic History 2001 v XIII  no 2  pp103-110 . (The same paper as word document)

16) Alternative option pricing methods based on the concept of insurance

Published In “Review of Economic Sciences” of TEI of Epirus, 5, 2004

(The same paper as word document)

 By Dr Costas Kyritsis        and              By Dr N. Antoniadis T.E.I. of Hpeiros  Arta, Greece

 In this paper it is  given alternative methods to the Black-Scholes method of option pricing, that give the later as special case. The alternative methods are similar to the methods of insurance policies pricing in actuarial mathematics. We leave open and  variable which model is chosen for the representation of the changes in the prices of the underlying asset. Numerical examples are given. The present method is compared with the traditional of Black-Scholes  and  are analyzed its advantages.

17)  “Optimal investment policies and oscillators of stock market  technical analysis. Application in the Impact of the war in Yugoslavia to  the Greek Stock market.”

(The same paper as word document)

By Dr. costas kyritsis  Software Laboratory  National Technical University  of Athens

Abstract: In this paper we analyze some price oscillators of stock market technical analysis as linear digital convolution filters. We review some of the theoretical published research on optimal trading policies in stock markets and we give an application of this approach in the negative shock impact of the war in Yugoslavia to the Greek stock market.

Key words: Portfolio Selection, technical analysis, stochastic optimal control, digital linear filters, time series. JEL C3, C4, C5


 Research ideas under development


 18) Coupled macroeconomic growth and exchange rates crises.From Win-Lose, to Win-Win interaction

By Dr Costas Kyritsis         University of Portsmouth  Faculty of Sciences and  Technology Dept. of Mathematics and Computer Science Fr. in Athens, Greece.


In this paper we formulate and study the interaction of the macroeconomic growth of two economic entities, that leads in to oscillations. Compared to the system of equations of a closed Economy of Hansen-Wright (1992) the present approach makes use the simplest possible system of equations that produce oscillations, and is a different system of equations. It is also a new and different system of equations for demand and supply interplay that leads to oscillations. This interaction usually occurs when the first of the two organizations or economy gives its output product as input resource  to the   second. We formulate it either as linear system or as a logistic non-linear growth system, with  the Volterra equations of Ecology, where the first organisation is the prey or host and the second is the predator or parasitoid. This implies a waving balance of the various domestic economies or organizations that fall in to such interactions and define in the economy reflecting pulsations that can be considered as part of the "ecological life" of the collective activities. We can derive these equations from probabilistic assumptions of coupling in the growth of populations, and described as Branching processes. We shall not present this derivation of the proposed equations of coupled growth, from assumptions on Branching stochastic processes, in this paper. If we reformulate the coupling interactions with linear equations then the qualitative dynamics of such a simplest system is   destruction of one of the two parts. The above is a characteristic case ofa win-lose interaction. We discuss how interactions under the spirit of win-win policies, are formulated as linear coupling that does not lead to oscillations.We give applications, 1) in the buying demand and selling supply of stock exchange markets and in general of any deman and supply interplay 2) in the interaction of the banking system and  the organizations, 3) in the  interaction to the stock exchanges and the real business of the organizations 4) in the  interaction to the stock exchanges and the banking system, 5) In the interaction of money (Liquidity) and gross domestic product in a close economy where in addition prices and risk-free rate participate in the equations 6) in the  interaction of  the exchange rate in the currency market and the balance of payments as determined by imports-exports, 7) in the  interaction of the 1st world economies and the 2nd world economies. We discuss the international monetary system of the floating exchange rate, in which the exchange rate is over determined by the speculation in the currency markets and is not so much determined by the gross national product and the risk-free rate of the domestic economy after the purchasing power parity principle. We discuss the resulting crisis like that of Mexico in the 80’s and the recent of Argentina. We suggest plausible cures, that are mainly a regulated by international law, floating exchange rate, within limits determined rigidly from the internal parameters in the domestic economy like that of the national gross product and bank’s risk-free rate.    


See also he very interesting Blog about how the over-debt is created in the monetary system


19)  Speculations about  electronic currencies, about  exchange rates, own-banking for each company, private web based exchanges, wellness insurance, charity  and other new methods in capital markets and macroeconomics, through the information technologies in the new millennium.

  By Dr Costas Kyritsis         University of Portsmouth   Faculty of Sciences and         Technology Dept. of Mathematics  and Computer Science Fr. in Athens, Greece.


In this paper we go one further step in suggesting solutions to exchange rates crises. We speculate on new procedural methods of stock exchanges, capital markets and banking that became possible in the new millennium, through the Internet, and Information Technology. The new methods should make the macroeconomics more robust, stable, clear in the economic concepts and objectives, while at the same time permitting even more flexible and fast handling of the demand and supply in the Markets. We speculate on the following new rules and methods:

1) Many International electronic currencies, but with mixed free exchange rates and regulated exchange rates. To avoid in the future for other countries exchange rate crisis like those of Mexico and Argentina, a return to the original concepts of Breton Woods about exchange rates is required. The present situation is a completely free-floating exchange rate, determined my the demand and supply. This is basically not wrong,  but if it is the only factor determining the exchange rate it, obviously creates an extravagant bias as far as it concerns valuation of the fixed assets, of a domestic economy. If we imagine a domestic economy as a very large company, it is as if permitting to valuate the total assets of the company only from the size of the sales of one only turnover! It does not seems fair. Therefore the suggested is a weighted average exchange rate

R=a*R(floating)+(1-a)*R(Domestic_Product_,_fixed_assets,_public_bonds_prices). In other words the final exchange rate is a weighted average of the floating exchange rate determined as it is by now through demand and supply, and an exchange rate defined though the gross domestic product and fixed assets of the domestic economy. The weight a is a Governmental or International decision. Nothing changes in the practice of Interbank transactions, in the  currencies, except that the effect of free demand/supply in the currency exchange rate changes is less. As practically within 3 months the term R(Domestic_Product_and_fixed_assets), is not changing, the variations of the exchange rates as we watch them in computer monitors are just reduced by an appropriate factor, that depends on the weight "a" too.

2) An alternative solution: The present demand and supply for a domestic economy's currency, is substituted with the demand and supply of domestic public bonds, of fixed price, so that each item bought is issued at the same time and each item sold is withdrawn at the same time. Thus buyers and sellers have transactions not between them but always with the central bank of the domestic economy. The return of the buyers of the fixed price public bonds are through dividends depending on the GNP, or on the balance of payments (import-exports ,etc). The capitalization of the financing of a domestic economy and its foreign currency reserves are thus floating, plus the uncertainty about the dividends, and not the price of its bonds or its currency rate, which is fixed. As alternative we may define the final currency exchange rate as a weighted average of the exchange rate as determined my supply and demand of the currency and the variable by supply-demand of the price of its bonds. As these two are often negatively correlated, the final exchange rate is more stable. The domestic economy is in this way is safer as far as its wealth is concerned, not endangering an exchange rate crises like that of Mexico in the 80's and Argentina's in the 00's, after an unlimited and panicked speculation on the currency. The Domestic economy would not let the minority of trading speculators, to determine the size of its wealth and capitalization through the exchange rate level. The present situation is, if put by an analogy in microeconomics, a situation where, vendors, and customers of a company  (analogue of foreign consumers and investors to the Domestic Economy), would determine, the price and value of the fixed assets of the company (analogue of fixed assets of the Domestic Economy), by the balance of Demand and supply on the products- outputs and inputs of the company (analogue of imports-exports and balance of payments). This "tightens" of values of the cycle of the turnover and sales with that of long term-capitalization and fixed assets, which is not really necessary, and in fact it has been proved very dangerous for crises in Domestic economies. G. Soros has already remarked on this weak point of the present system of exchange rates and has given long interviews about its role in generating exchange rate crises. Of course such a new suggested system would still not protect a domestic economy, from bankruptcy due to bad economic planning and performance or other wrong activities. The Purchasing Power Parity Principle , and the Interest rate parity, as far as investments in the public bonds, have better chances to hold, as the Domestic economy, can adjust the rate of return on the bonds, in the form of dividends, according to the risk-free rate, and inflation, so as to have in all domestic economies practically almost the same rate of return. (In the present system this was regulated through the exchange rate floating by Demand and supply). I addition in rare cases from time to time the Domestic Economy may adjust the fixed exchange rate (if it is not the case of one universal currency) so as to be closer to a Purchasing Power Parity Principle. .

3) Derivatives exchange markets can still run in such a system, E.g. futures and options, defined on all levels of leverage, from leverage 1, (which would be equivalent as far as the risk is concerned to the older buying and selling of the currency units), till the present levels of leverage, and margin. The futures and options are cleared, at the expiration date, on the total number of bond-items of the domestic economy on that date, and on their prices that are fixed.

4) Own Banking of Large Companies. Large companies get rights similar to banks. In other words the public can deposit money and take a deposit rate, while the company can invest or lend these funds. A percentage of the capital of the company is thus financed in this way. In this way every company that meets some qualifications (similar to the ones required to issue bonds or stock exchange securities) may have its own banking system. It can keep say for reasons of liquidity and to meet the floating of the demand-supply, as the banks do so with the deposits, the 20% of the capitalization, and use the rest 80%. The creation in this way of an "own-banking”, for every company, would make the economy, even more efficient, flexible, and stable. This would be the analogue in macroeconomics, to the advance in Politics from the age of Aristocracy-Oligarchies to Democracy the central economic power of banks, is distributed, to local "small-banks", one for each company. See also

5) Derivatives exchange markets can still run in such a system, E.g. futures and options, defined on all levels of leverage, from leverage 1, (which would be equivalent as far as the risk is concerned, to the older buying and selling of the companies securities), till the present levels of leverage, and margin of the derivatives. The futures and options are cleared, at the expiration date, on the total number of bond-items or shares of the company on that date, and not on their prices, which is fixed. Those that want to risk fast gain or losses, must trade in the Derivatives markets.  As alternative the underlying of the derivatives could be the dividend rates of such bonds.

6) This new system of demand-supply for the capitalization of a company, and the speculation through derivatives on it, can be implemented with private, capital-markets, and derivatives-markets or exchanges The advantages for the companies in  such a more rational capitalization system, may create increasing demand for smaller companies to participate in such private-capital markets, and permit successful emergence of private capital markets.

We discuss the stability, and Freedom, advantages of these new methods in the societies. Although this system may seem almost the same with the present, this minor difference makes a big change in the stability, efficiency and fairness in the world of investments.



  0 The main purpose of this research is to show how the principles of Pareto in macroeconomics that state e.g. “the profits of one part of society are not necessarily the losses of an other part of society” can be modeled and proved with simple linear mathematical models. A classical simplistic example is the next: Imagine the economy of an island of 10 inhabitants, that it has a small hill with forest and a river , a small lake, a green field, and many small gulfs. A win/lose approach to wealth would correspond to the choice that all inhabitants rush  to cultivate the green field, and produce agriculture goods. Obviously in such a choice the wealth of each man would antagonize with the wealth of an other as all are concentrated only only the green field which becomes a scarce resource. It is a win/lose solution of a zero-sum game. As an alternative choice in the Pareto principle and a win/win approach would be that the inhabitants diversify in  wooden crafts from the forest, in water mills from the river and the lake and in fishing from the lake and the sea. Obviously the wealth of each adds to the wealth of an other and to the total domestic product and wealth of the island. In the same simplistic example we may realize how unemployment is created and can be reduced. Assume that all the 10 inhabitants are fishermen, fishing each with a fishing-line. As technology changes a new technique of fishing emerges which is called fishing net. Now only two inhabitants are needed, one to drive a little boat and an other to handle the fishing net. The volume of  fishes only from the two inhabitants with the net is the same with the volume of fishes produced by all the 10 inhabitants with fishing lines, so 8 of the inhabitants remain unemployed. We have now 80% unemployment. The governments of the island can choose a socialistic approach in which it puts high taxes to the 2 fishermen with the net to give to the 8 unemployed. This could be a solution but it does not help development of the economy of the island. An alternative solution to the problem of unemployment is to discover and create new goods and services to absorb the unemployed. E.g. The 8 unemployed inhabitants could learn how to make furniture from the wood of the little forest and to cultivate the field in the island. This would not only give them the necessary wealth but a wealth that does not antagonizes but supplements the wealth of the other inhabitants , contributing so in a larger total domestic product of the island. It seems that the correct solution would involve  a compensation of both alternatives a short term application of the "socialistic" in a smallest measure, just to heal the first crises and then a long term effort for the second which really solves for even better the problem and it is certainly creative for the society.

 We use input-output equations in a more comprehensive way than Leontief. From this point of view the research can be classified as anew category of equilibrium models, although, the only strictly speaking the only “equilibrium” is just that all accounting transactions clear-out . On the other hand such formulations can model optimal growth under specified objectives. I was inspired for this approach from general equilibrium models of economies within the European Union that tried to estimate the “costs” in the EU economy of reducing the CO2 emissions.

The present models prove that all sectors or domestic economies can profit , and that the losses of one sector are not necessarily the gains of another sector. Similar applications can be described with a model of interaction of EU and United States economies. Therefore from the game theoretic approach are considered a non-zero sum games.

  1. This paper contains  a miniature model of 16-24 equations , based on linear system, or linear programming input-output equations.

We chose linearity so as to have the mathematical part soluble and concentrate on the economic interpretation. We chose therefore the Leontief approach except that in the present paper we are including both physical products, together with financial services (money flow)in the same equations.

  2. We first defined a network, for all transactions, and productions. For any network there is a vector-space (over Z2 Galois field) of cycles, and a dual space of cocycles, and also a matroid of circuits which is purely algebraic , that describe all dependences, with concepts like "base", "dimension", even if someone puts nonlinear economic equations for the network. The later linear system of input-output (and dual of output-input) is simply an isomorphic replica of this structure in some abstract category. To every cycle corresponds exactly an equation.

  3.  We used only one (linear) household,  a (linear) industry, a (linear) bank, and a (linear) Government. The behavior of each of these entities is left completely open , and is set by the technology, and flow-distribution decision coefficients on the network of flows.

(behavior of household: labor, purchasing, savings, borrowing, investments etc and similar for industries, banks, government). In a computer interface they are determined interactively by the user. The assumption of linearity is reasonable for a small range of the quantities and time duration (this is true for the linearity of accounting equations too). Linearity gives constant returns on scale.

  4. To preserve the technique of duality of Leontief  we used so many variables so as to have one equation for each output product or service, and not one equations for each entity.

  5. The equilibrium here has simply the interpretation that "all transactions clear-out"

  6. For a household, purchasing of tangibles, borrowing, investments , and fixed assets growth are all included.

  7. For industries, and banks,  dividends of equities (profit), and reinvestment growth of fixed assets are included, as well as capital mobility

  8. For Government, are included ,issuing of money , taxes, and fixed assets growth, too.

  9. The Leontief duality is represented here not as a duality of flow of  tangible products and finance, but a duality based on that each transactions has two flows, the one is the service or good (including funding, investments etc) and the other the exchanged price of it. Of course interest rate is the price for money, and so are dividends. Taxes are the prices of government services.

  10. The dual system is a system of prices (including interest rates, dividends, taxes etc), and there is one (accounting) equation for each product or service (including investments, liabilities, growth of fixed assets, and money issuing), and  not one only accounting equation for each entity.

  11. The system can be solved either as a linear system or as linear programming system. In the latter case we may put inequalities to scarce resources, like labor with limits both upper as true constraint, and a lower only for assessment of existence of unemployment.

The objective can be either a maximization of weighted average of growth of fixed assets or wealth and aggregate domestic product, or a maximization of pre-emptive ordered pair of them

(first we maximize the one and then on the remaining degrees of freedom the other).  This is only a static one-period optimization. For an intertemporal dynamic optimization, we may require to find as optimization solution the weights (static social welfare  policy) in the static objective function so as to maximize final wealth or a linear utility function of it. The evolution or multi-step (period) development of each entity (Household, Industry, Bank, Government-state ) can be represented with cash flow systems that at each time step or period  the cash flow is the increase or decrease of assets, equities , and liabilities. In this way each entity reflects the elementary functionality of banking.

From the above we deduce that the evolution of solution prices from period to period, derives the inflation rate too, changes in the interest rate, changes in profitability, growth etc.

  12. Thus equilibrium is used here both with optimality. Equilibrium is only the minimum constraint of "all transactions clear-out", while the behavior of households, industries, banks, and Governments is not locked by any theoretical assumption, but is set by the user at each period. Optimality is in the context of social welfare, and any static optimal solution is also Pareto optimal (Pareto approach: " The profits and wealth of a part of society do not need to be a loss to an other part of society").

  13. The spirit of this optimality is a win-win approach, as the issuing of money (monetary policy) permits solutions where all entities have a non-negative growth and profit, although not equally distributed (usually the smaller in size entities have larger growth rate, compared to larger entities, but vice-versa at  values, not rates). Thus it is not a zero-sum game, although it may be defined if we want as  a zero sum game  if we put nature as the loosing part, and force conditions of zero sum game.

  14. An even simpler system can be written for two domestic economies or e.g. European Union/United states, where again a win-win linear optimal solution is possible, with both sides growing, although not at the same rate. The exchange rates of the currencies is derived from this system, by a simple formula from the linear equations. Such pairs can be considered also as matrices of linear games, and its solution as solutions according to optimization of an objective.

 15. The effect of discovering and creating new goods and services can be simulated in the model by adding new types of industries of  new goods and services that absorb the unemployed. The final solution can result with higher total gross domestic product. This shows how the problem of unemployment can be solved creatively with a result of improvement of the domestic economy.

16. The previous model  can me easily solved by Excel's solver. For a large version of it, the linear system approach (Recursive numerical algorithms) is tractable as far as computer complexity is concerned, while for a linear programming approach, the Carmakar's algorithm is required instead of the simplex algorithm (the latter solves usually up to 6,000 variables/equations while the former 160,000 or more). The model can be developed as a user interactive computer game on a site in the Internet.  

17. This simple linear macroeconomic model, can be formulated as a stochastic process too, if we assume that the independent variables, e.g. volumes of production of goods and services are random variables. Then the linear deterministic equations above are used simply to calculate the dependent random variables. 

18. The input random variables can be set to contain random cycles that come from the supply of agricultures raw materials, and conditioning of human activities , labor, energy consumption etc from meteorological cycles. Thus cycles of day-night, week, month. year's seasonality, 11-years sunspot cycles etc can be included in the model. The author suggest 12 cycles at 12 different time scales, that are measurable fertility cycles  of the biosphere, and measurable meteorological cycles too. These cycles have fixed average period connected to fixed periods of earth and other celestial bodies (like moon, sun etc) cycles. A concise table of  these cycles as can be measured in meteorological and ecological magnitudes can be found in the page for the meteorology in the present site. 

 19. The author has made extensive studies with data, spectral analysis, and simulation that confirms the existence of these cycles both in the meteorological and macroeconomic magnitudes. It is not trivial to prove that if the independent production volume of input resources and independent input prices have a spectrum with discrete counter part on the above 12 spectral areas then the dependent production volumes of goods and services and dependent  prices would have also a spectrum with the same structure. In other words the above macroeconomic structure leaves invariant the spectrum structure as far as the existence of the above 12 stochastic periodicities is concerned. The value of realizing the existence of these celestial and eternal cycles in macroeconomics is great: By realizing that supply of raw material shall follow such cycles, domestic economies can arrange for a smoothing out of them by storing excess raw materials if possible. Also by realizing that the demand for energy, due to these cycles in meteorology , will follow similar  these cycles too, we can arrange again for a smoothing out by storing if possible excess energy or arranging for the possibility of excess production. The ancient story in the Old testament of the Egyptian Pharaoh's dream  and its explanation by  Joseph, of the 7 fat and 7 slim cows is an example of how such knowledge can be  used. The effect is higher stability and equilibrium of the macroeconomic systems. In addition application of these cycles that modulate the hazard rate of events insured by insurance companies, improves the pricing methods of insurance contracts, make insurance business safer.

20. Such a stochastic cycles quantitative description, reflects the permanent exogenous conditioning of macroeconomics, by causal sequences that fall in the  area of study of ecology, meteorology, and eventually astronomy. It seems  that such an exogenous  causal source of macroeconomic and business cycles is the only truly permanent and stable that can lead to sound and wise scientific description. The difference of the above approach as compared to the standard approach in which we intent to forecast the particular year or month is great!

In the usual approach are used mathematical or statistical models to forecast the particular season or year or 5.5 year horizon etc, while in the present approach is anticipated the generic and eternal cycle of season or year or 5.5 year horizon etc. The mathematics are completely different too as the dynamics of the production of the particular period is considered only as "noise" to the dynamics of same generic or eternal period.

The main value of knowing and measuring eternal cycles in the macroeconomic systems, that have their source in exogenous to society sources  (meteorology, nature etc) is that the society can reduce the variance by provisions.

References for cycles: The next books are excellent references for the old concept of cycles in economics 1) "Weather cycles (real or Imaginary?)" by Williams James Burroughs 2nd edition Cambridge 2) Economic Value of Weather and Climate Forecasts (Hardcover) by Richard W. Katz (Editor), Allan H. Murphy (Editor) Cambridge University Press 1997 3) Business Cycle: Their law and cause By Henry Ludwell Moore (Columbia University)  3) Business Cycles The Nature and Causes of Economic Fluctuations Books Thomas E_ Hall 4) Business Cycles, Indicators, and Forecasting (National Bureau of Economic Research Studies in Income and Wealth) Books James H_ Stock, Mark W_ Watson

  Key words Macroeconomic Models, General Equilibrium models, Input-Output equations, Pareto Optimality, Win/Win game policies, European Union macroeconomic models, Planetary macroeconomic models, business cycles, macroeconomic cycles.

 21) Different roles , definitions and concepts of money at different organization levels in society.

Wealth, charity, welfare and public goods.

By Dr Costas Kyritsis (2005)  


In this article we analyze how the role and concepts of money changes essentially as we move from low and simple structure organization levels in society (like transaction, individual, enterprise) to more complex (like large groups of companies, public economics, domestic economy currency etc). Charity and public services is discussed in relation to the definition of money at the level of enterprise and domestic economy.  The next table gives a sketch to the different definitions of money

Organization level in society

Role , value, and definition of money


Valuable object due to contained precious metal (e.g. coins from gold or silver)

1) Transaction

Means of exchange

2) Individual

An informational measure of personal activities awareness and a way to freedom of activities and choices. Also a measure of “share” in the social power ,goods and services.There is practically an average size  of relevant wealth. All surplus wealth, plays the role of enterprise money in the next category.

3) Enterprise

"Raw material" to organize, hire people and "seed" for organizational and group activities growth and multiplication. Also a measure of “share” in the social power and goods, and a special type of information.

4) Single domestic economy

A measure of internal circulation of the goods and services, and a special type of information.

5) Many domestic economies with many currencies

A measure of external interaction of the two economies as mutual flow of goods and services and a method of indirect pricing of domestic goods and services of the one economy from the goods and services of the other economy 


See also he very interesting Blog about how the over-debt is created in the monetary system



By Dr Costas Kyritsis  School of Management and Economics  Dept. of Finance and Auditing  Technology Institute of Epirus  Preveza, Greece

  ABSTRACT     In this short note we discuss the gap of the principles of education as seen from the academic world and as seen from successful businessmen that tried to communicate their experience. In particular we focus on the subjective experience on the difficult path of financial success and its background emotional qualifications (EQ) in the individual’s consciousness. The results are a challenge and a surprise to the academic common sense. JEL A2 Key words: Teaching Economics, Emotional Intelligence, Education.

(The same paper as word document)


23) The Principle of Macroeconomic-Microeconomic structural and dynamic correspondence


By Dr Costas Kyritsis (2006)

In this paper we develop a bold interpretative principle , according to which any macroeconomic system has a bold correspondence in its structure to a microeconomic system (e.g. business, company). E.g. the Input-Output equations of Industries of Leontief, would correspond to similar equations of Production Departments or Profit centers of an enterprise. Under such an interpretative principle, many of the old macroeconomic debates about the relation of the observable macroeconomic magnitudes like, rates, inflation, unemployment , growth, prices etc are resolved under new understanding. This principle can apply also in to a similar correspondence in the structural equations of an Enterprise (mid-scale economics) and a Household  (micro-scale economics). We do not claim that there is a full self-similar correspondence , but only a  correspondence that when it is from larger scale to shorter scale it looses information and detailed structure, but some of its structure can remain invariant. In the terminology of the mathematical theory of categories, it would be an homomorphism rather than isomorphism. The same principle can apply to larger macroeconomic entities like union of domestic economies e.g. European Union, and a single national domestic economy. The basic household economics equations, and enterprise accounting system equations (5 basic equations) , give rise to corresponding macroeconomic systems of equations.

From a mathematical point of view the similarity correspondence is quite more clear as in all three or four cases (two in macroeconomics, microeconomics and Household) similar linear systems of input-output equations are formulated. Especially for the nano- or micro-scale economics of household behavior we introduce a , I think a revolutionary, conceptual innovation: The single household behavior is not described by a single household utility function, but by many utility functions (vector utility function of a single household) that are linear functions of resources and other household's utility functions of the same household. E.g. we may postulate food utility function, cloths utility function, entertainment utility function, education and personal development utility function, leisure utility function , and in addition utilities attached to achieving goals per time scales like day's goal achievement utility , week's goal achievement utility , month's goal achievement utility, quarter's goal achievement utility etc. I believe that in this way the behavior of the individual is better described and is not put to a monolithic totalitarian single scalar utility function. Not all are comparable in the "feelings" of the individual with a totally ordered utility function. This multi-utility householders behavior is I believe appropriate for the emerging individual's globalization behavior, that for the moment we observe for individuals that run globally successful dotcom internet companies. The scales are not only two, Domestic Economy and enterprise, but rather at least four: The global international realm, the domestic national economy (the latter two are traditionally studied in Macroeconomics), the enterprise and the household (the latter are usually included in the studies of microeconomics).


24)  The Rainbow model :  The effect of natures multi-scale cycles on the stochastic growth of the wealth of nations.

By Dr Costas Kyritsis (2006)

In this paper we describe the sequence of causalities from nature's 12 cycles (from 11 years to 5 minutes) that influence economic cycles. The sequence of  effects may belong to many different sciences and disciplines like astronomy, meteorology, ecology, and economics (macroeconomics and microeconomics). The 12 cycles include the 11-years cycle of solar activity, that is reflected to weather cycles and ecology cycles (detectable e.g. at tree-rings , rainfall, and water level of lakes) as well as the year cycle. All the 12 cycles already have been   studied and detected in modern meteorology. The stochastic process that is used to formulate the random influence of matures cycles to economy, is an entirely new mathematical concept and is therefore a new discovery also in the science of mathematics and statistics. It has the features of multi-layer causality and memory, "vertical" or interlayer laws as well as "horizontal" or time recursive laws. The effect of natures cycles in the economy is not necessarily cycles but something simple, and at the same time random enough to reflect most of the observable charts and economic data. Some of the hidden harmony in economy may depend on natures cycles but the observable is not always a visible cycle. We concentrated only on the  effect of natures eternal cycles. All the  non- temporary endogenous cycles of the economy, tune to the  eternal exogenous nature's cycles. Although many of the economist would focus on endogenous causalities in social economics, the exogenous (nature) and endogenous (society) effects, essentially coincide in timing. It took the author 7 years of intense study of economics data and computer simulations to conceive the stochastic process of Rainbow, and the implicated philosophy  in the causes of economic phenomena. Such a knowledge that links the design of the action and changes in the solar system, and earth, to the design and patterns of economic action in societies, is developed so that all nations great and small can balance, and protects their life energy and wealth resources, in an ever changing world. In view of the expected extreme weather phenomena of the first part of the 21st century it seems that it is an even more valuable knowledge. The "world game" of international interactions is definitely played better with better world-leverage for each economy after the realisation of the economic significance  of the knowledge of the Rainbow cycles. It is a basic chapter in an "operating manual of spaceship earth" , as Buckminster Fuller would put it, so as to lead to a intelligent  living of individual human beings, that is healthy, abundant, fair, safe and satisfactory for  the body, the feelings , the intellect, and the metaphysical element. This is to be contrasted to a suicidal life of nuclear wars threat, based on economic controversies. 


Let me quote this great 20th century thinker, that has a kind of thinking that would support the synthesis of sciences and causalities of macroeconomic phenomena in the above research. He is the famous to many Buckminster Fuller, in his manuscript "Grunch of Giants"

"Before humans could be designed to occupy it, planet Earth had to be designed. Before planet Earth could be designed, the solar system had to be designed. Before the solar system could be designed, galaxies had to be designed. Before special-case galaxies could be designed, special-case macro-micro Universe, all its atoms and molecules, gravity, and radiation had to be designed. Before any realizable designing was possible, it was cosmically necessary to discover and employ the full family of eternally coexistent and synergetically inter-augmentative, only-by-mathematical-equations expressible, intercovarying, generalized principles governing the generalized design of eternally regenerative scenario Universe. And before all recognition of the eternal generalized principles and their inherent design-science functions, it was further necessary to have:

  1. The design of an eternally regenerative, radiationally expansive and gravitationally contractive, everywhere and everywhen complexedly intertransforming, nonsimultaneously episoded, scenario Universe.
  2. The generalized design of galaxies of entropic matterinto-energy as radiation-exporting stars and generalized star systems of planets serving syntropically, as radiation-into-matter importing planets.
  3. The design of planet Earth as the Sun-orbiting, biosphere-protected, and oxygen-atmosphere-equipped incubator of DNA-RNA design-controlled biological life and of that life's photosynthetic conversion of entropic radiation into syntropic, orderly hydrocarbon molecules and a vast variety of hydraulically compressioned, crystallinely tensioned, exquisitely structured biological species omni-inter-regenerating as an ecological omni-life and human-thinking support-system.
  4. The eternal mathematics — numbering and structuring. The eternally extensive mathematical spectrums of frequencies, wave lengths, and harmonic intervals.

Only thereafter could those human beings progressively re-evolutionize exclusively by trial-and-error enlightenment, from their born-naked state of absolute ignorance, to discover their scientific-principle-apprehending minds and thereby (now for the first possible moment in history) to glimpse humanity's semi-divine functioning-potential as local-Universe critical-information-gatherers and localUniverse problem-solvers in support of the integrity of eternally regenerative Universe."

"The Things to do are: the things that need doing, that you see need to be done, and that no one else seems to see need to be done. Then you will conceive your own way of doing that which needs to be done — that no one else has told you to do or how to do it. This will bring out the real you that often gets buried inside a character that has acquired a superficial array of behaviors induced or imposed by others on the individual. "Letter to "Micheal" (16 February 1970) Micheal was a 10 year old boy who had inquired in a letter as to whether Fuller was a "doer" or a "thinker".

"There is an inherently minimum set of essential concepts and current information, cognizance of which could lead to our operating our planet Earth to the lasting satisfaction and health of all humanity." From Synergetics 1, The wellspring of reality.  (see also about "the world game" in, and )

Buckminster Fuller, was a global-thinker of the middle of 20th century worked so as to create a mimimal system of concepts, and processed contemporary information , in cosmology, philosophy and metaphysics, physics, ecology, engineering, architecture, design  poleodomia, economics, sociology, politics, education, etc so that people in any nation, can think, feel, and act to a living that does not lead to the extinction of life on all or part of the planet Earth.

Remark : For further ideas on the rainbow process see the blog




By   Kyritsis Costas , Sotiropoulos Ioannis, Gogos Christos, Kypriotelis Efstratios.

Department of Finance and Auditing , TEI of Epirus, Preveza, September 2007 Greece


  In this paper we prove and analyze the effect of  the 11 years sunspot, and global climate cycle, on the volatility of the prices of Stock Exchanges. We predict an increase of the prices from the present time (2007) till 2011, a next major maximum of the prices during 2010-2011 and a fall of the prices for the period 2011-2017. We discuss sequences of causal explanations based on the balance of demand and supply and comment on the general value of such an omniscience wisdom that  involves at least five different sciences.


The paper as word document

Remark 1 The Journal Archives of Economic History is an Internationally accredited Academic Journal . This is proved as it can be found in the International Database  ECONLIT which is the standard database of economic literature in most University Libraries.

Remark 2: For further ideas on the rainbow process see the blog