Komissarov Nickolai
Faculty: Computer information technologies and automations
Speciality: Is information operating systems
Theme of master's work: Computer subsystem of optimization of a portfolio of securities
Leader of work: prof. Sporuchin Viktor Yakovlevich
The author's abstract
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Action course change
Urgency of a theme of research.
The urgency of a theme of research proves to be true a current situation in the share market of Ukraine. Today banks, the broker companies, private investors, Internet traders sped up work in the field of formation and management of an investment portfolio. The urgency of the chosen theme proves to be true promptly growing quantity of nonprofessional participants of a securities market and necessity arising at them to use a professional knowledge about use of methods of the analysis of a securities market which could help to be guided in difficult processes of the market. Not less actual problem is working out of intellectual trading system supporting decision-making at all stages of management of a portfolio of securities on the basis of knowledge the participant of a securities market.
The given circumstance causes of carrying out of fuller system analysis theories and puts a problem of working out of methodical maintenance of managerial process by a portfolio of the securities, based on reproduction and imitation of processes of intellectual activity of the participant of a securities market, and creation on its basis of intellectual trading system for increase of a management efficiency by a portfolio of securities.
Object of research - managerial process by a portfolio of securities.
Object of research - working out of models, the qualitative and approached methods, algorithms of management of a portfolio of securities taking into account purposefulness of processes and in the conditions of uncertainty.
The purpose of dissertational research is increase of efficiency of managerial process by a portfolio of securities by increase of efficiency of decision-making on the basis of information base áîëüøåé capacities, and also decrease in not system risks. For achievement of the given purpose following problems have been put:
– To generalize the domestic both foreign theory and practice of management by a portfolio of securities, to investigate models, methods and the algorithms used at various stages of management by a portfolio of securities;
– To develop indistinct model of the emitter of a valuable paper on which basis to create a technique and algorithm of calculation of a comparative and classification rating estimation of securities on groups with certain investment qualities;
– To develop a technique and algorithm of an estimation of results of the technical analysis in the conditions of uncertainty and the uncertainty, a market model including situational;
– To develop conceptual model of system of support of decision-making at management of a portfolio of securities on the basis of the developed models, techniques and algorithms.
Application kvuzi-statistic gives wide open space for application of indistinct descriptions for modeling of laws on which this or that set of supervision is shown. In terms of the indistinct description from system formation of exact values of an estimation of probabilities, and the task of a settlement corridor of values of predicted parameters is required not. Then the expected effect is estimated by the expert also as indistinct number with the settlement disorder. Here there are engineering advantages of the method based on illegibility since the system operates not with indirect estimations where probabilities concern also, and direct design data about disorder of parameters that is well-known practice of the interval approach to design estimations.
Applying is indistinct-logic descriptions for a problem of formation of a share portfolio it is possible to consider that the income on a valuable paper (Central Bank) is casual, its exact value in the future is not known, and the likelihood description of such grade of accident is not quite correct, as the description of profitableness of the Central Bank pertinently to use triangular or trapeze kind indistinct numbers, modeling the expert statement of a following kind: “ Profitableness of the Central Bank on termination of possession term it is expected it is equal and is in a settlement range [r1, r2] ”. Here the expert refuses the likelihood description of profitableness, cuts low probability casual outcomes from two parties from expected value and forms a settlement corridor in which level of profitableness of the Central Bank is expected, thus for the expert accepts either the most expected, or average value of profitableness in a settlement corridor. Function of an accessory of indistinct number has a triangular appearance if degree of subjective confidence of the expert concerning profitableness is equal to zero outside of a settlement corridor of values of profitableness, and the maximum of this confidence equal to unit, is reached in a point. The expert is convinced, that will obviously get to any settlement corridor of profitableness how borders of this corridor varied.
If profitableness of the Central Bank - triangular indistinct number, and profitableness of a portfolio - a linear combination of profitableness a component the kind of profitableness of a portfolio also is known.
Let R'= (r1i, r2i) - profitableness on i the valuable paper, triangular indistinct number. Then profitableness on a portfolio:
R' = (R min=sum Xi*r1i, R' = Xi*R'i, Rmax = sum Xi*r2i), i=1,...,N
Sum Xi=1 , where {Xi} share price distribution of papers in a portfolio,
R' - Also is triangular indistinct number.
Now fixing - demanded level of expected profitableness of a portfolio and manipulating a vector {Xi}, it is possible to achieve a minimum of risk of investments. Record of this problem:
{Xopt}={x} Risk -> min, R=R'
Where - function of degree of risk of an inefficiency of the investments, calculated with use of the device of indistinct mathematics.
This problem is a dual problem of nonlinear programming to a problem in the following record:
{Xopt}={x} Risk -> max, R= const
This problem is similar to problem Markovic, only as a risk factor the standard deviation of a portfolio, and degree of risk of an inefficiency of investments acts not.
Let's estimate triangular parameters m, s by a maximum principle true kind. Let at us is kvuzi-statistic profitable nesses (r1, … rN) capacities N and the histogram corresponding to it (n1..., nM) capacities M. For this kvuzi-statistic we select two-parametrical normal distribution, being guided by criterion
Credibility
Where ri. Answering to i column of the histogram settlement value of profitableness.
It is a problem of nonlinear optimization which has the decision
And m0, s0. Arguments of maximum F (m, s), representing a control point. We will choose level of cutting off F1 <F0 and we recognize all likelihood hypotheses plausible if the corresponding criterion of credibility lays in a range from F1 to F0. Then all plausible likelihood hypotheses are answered with set of vectors A ‘ which in two-dimensional phase space represents convex area with nonlinear borders.
Let's enter in this area a rectangle of the maximum area, which side to in parallel phase axes. Then this rectangle represents truncation A ‘ and can be described a set of interval ranges on everyone a component
We name A "a zone of limiting credibility. Certainly, the control point gets to this zone, that is is carried out
That follows from an inimicality and smoothness of function of credibility. Then we can consider numbers m = (mmin, m0, mmax), s = (smin, s0, smax) as triangular indistinct parameters of density of distribution j (·) which and in this case looks like indistinct function.
Application of indistinct sets at the account of initial uncertainty concerning incomes under securities - rather perspective direction of the analysis of efficiency investments. The Expert-analyst at use of this approach is relieved of necessity to form likelihood forecasts for rather shaky information basis when the behavior of traded securities does not possess character of statistical casual processes. It is enough to expert to make an assumption about a settlement corridor in which it is expected the future income on the Central Bank fluctuates. At these elementary assumptions it is possible to estimate degree of risk of an inefficiency investments and to construct procedure on minimization of this risk.
The literature
1 METHODOLOGICAL BASES of MODELLING of FINANCIAL ACTIVITY With USE of is indistinct-PLURAL DESCRIPTIONS St.-Petersburg the Dissertation Nedosekin Alexey Olegovich 2003
http://www.mirkin.ru / _ docs/doctor005.pdf
2 Ponomarev A.JU. application of indistinct sets for a risk estimation ïîðòôåëüíûõ investments. http://journal.seun.ru/j2003_1r/Economy/economy.htm
3 MODELLING OF MANAGERIAL PROCESS BY THE PORTFOLIO OF SECURITIES IN THE CONDITIONS OF UNCERTAINTY
Frenkel MICHAEL Astrakhan - 2006 ã