Optimization of the Investment Portfolio in the Conditions of Uncertainty

Portfolio analysis exists, perhaps, as long, as people think about acceptance of rational decisions connected with use of the limited resources. However the occurrence moment of portfolio analysis can be dated precisely enough is having connected it with a publication of pioneer work of Harry Markovittz (Markovitz H. Portfolio Selection) in 1952. The model offered in this work, simple enough in essence, has allowed catching the basic features of the financial market, from the point of view of the investor, and has supplied the last with the tool for development of rational investment decisions. The central problem in Markovitz theory is the portfolio choice that is a set of operations. Thus in estimation, both separate operations and their portfolios two major factors are considered: profitableness and risk of operations and their portfolios. The risk thus receives a quantitative estimation. The account of mutual correlation dependences between profitablenesses of operations appears the essential moment in the theory. This account allows making effective diversification of portfolio, leading to essential decrease in risk of a portfolio in comparison with risk of the operations included in it. At last, the quantitative characteristic of the basic investment characteristics allows defining and solving a problem of a choice of an optimum portfolio in the form of a problem of quadratic optimization.

Uncertainty and Fuzzy Sets: Classifying the Situation

The so called “Plural Uncertainty Model” is considered, in which statistical, maxmin, interval and Fuzzy model of uncertainty are embedded. For the last case external and internal contradictions of the theory are investigated and the modified definition of the Fuzzy Sets is proposed to overcome the troubles of the classical variant of Fuzzy Subsets by L. Zadeh. The general variants of logit- and probit- regression are the model of the modified Fuzzy Sets. It is possible to say about observations within the modification of the theory. The conception of the “situation” is proposed within modified Fuzzy Theory and the classifying problem is considered. The algorithm of the classification for the situation is proposed being the analogue of the statistical MLM(maximum likelihood method). The example related possible observing the distribution from the collection of distribution is considered.

Towards the Problems of an Evaluation of Data Uncertainty in Decision Support Systems

The question of forming aim-oriented description of an object domain of decision support process is outlined. Two main problems of an estimation and evaluation of data and knowledge uncertainty in decision support systems – straight and reverse, are formulated. Three conditions being the formalized criteria of aimoriented constructing of input, internal and output spaces of some decision support system are proposed. Definitions of appeared and hidden data uncertainties on some measuring scale are given.