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.

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Efficient Control in Multistage Stochastic Optimization Problem

AMS subject classification: 90C31, 90A09, 49K15, 49L20.

Computer Processing of Medieval Slavic Sources in the Institute of Literature at BAS Repertorium Project (1994–2004)

Mixed-content miscellanies (very frequent in the Byzantine and mediaeval Slavic written heritage) are usually defined as collections of works with non-occupational, non-liturgical application, and texts in them are selected and arranged according to no identifiable principle. It is a “readable” type of miscellanies which were compiled mainly on the basis of the cognitive interests of compilers and readers. Just like the occupational ones, they also appeared to satisfy public needs but were intended for individual usage. My textological comparison had shown that mixed- content miscellanies often showed evidence of a stable content – some of them include the same constituent works in the same order, regardless that the manuscripts had no obvious genetic relationship. These correspondences were sufficiently numerous and distinctive that they could not be merely fortuitous, and the only sensible interpretation was that even when the operative organizational principle was not based on independently identifiable criteria, such as the church calendar, liturgical function, or thematic considerations, mixed-content miscellanies (or, at least, portions of their contents) nonetheless fell into types. In this respect, the apparent free selection and arrangement of texts in mixed-content miscellanies turns out to be illusory. The problem was – as the corpus of manuscripts that I and my colleagues needed to examine grew – our ability to keep track of the structure of each one, and to identify structural correspondences among manuscripts within the corpus, diminished. So, at the end of 1993 I addressed a letter to Prof. David Birnbaum (University of Pittsburgh, PA) with a request to help me to solve the problem. He and my colleague Andrey Boyadzhiev (Sofia University) pointed out to me that computers are well suited to recording, processing, and analyzing large amounts of data, and to identifying patterns within the data, and their proposal was that we try to develop a computer system for description of manuscripts, for their analysis and of course, for searching the data. Our collaboration in this project is now ten years old, and our talk today presents an overview of that collaboration.