Abstract: The object of study in the article is the credit, however it does not concern its economic essence regarding both the creditor, and the borrower. The key aspects of studу concern the mathematical foundations for modeling the  phenomenon of related borrowers. The author stars her research by analyzing economic maintenance of a phenomenon of being related, while directly giving strictly mathematical interpretation to the economic terms, which she employs. Further the author explicitly considers functional and stochastic aspects of coherence of borrowers, showing continuous connection among these aspects. The methodological basis of a research is formed with the set-theoretic and probability-theoretic approaches. Application-oriented aspects of the loan portfolio modeling are explained in terms of the algebraic theory of risk. The graphic illustration of the main results of operation is based on classical submissions of the Cartesian product of finite sets and on traditional (quasi) trees of classification. The key result of this  study is revealing of the complete mathematical list of possible options for the coherence of borrowers in the functional and probability-theoretic contexts. At the same time the article contains detailed descriptions of all possible relation options within the object field of study. This a  novel relation classification. Similar studies are not found among either Russian, or foreign studies so far. Another result of this study is a practical one, since some of the received ratios can be used in order to form efficient algorithms for the direct analysis of risk processes within the complicated systems.

Abstract: The subject of the research is the methods of optimization, in particular, methods of random search for the global extremum of functions. The object of the research is the problems of the random search connected with the replacing the flow of equally distributed truly random numbers with pseudorandom sequences. The authors have created a simulative example that can clearly demonstrate limitations of the method of equal random search in case when the period length of a pseudo-random sequence used is comparable to potentially achievable number of target function calculations in the given group of traditional calculations. The authors demonstrate that there are serious limitations of the random number generator installed in the VBA-subsystem of the Microsoft Office package when using the option of random search in algorithms. When synthesizing the model target function, the author has used the methods of algebra and analysis. The main results of the research is the statement about impractibility of using the pseudo-random number generator installed in the VBA-subsystem of the Microsoft Office package in random search algorithms and recommendations on how to replace the installed sensor with the new generation generators such as Mersenne twister.