О применении нечетких чисел при оценке опционов
There is no accurate answer for the question, which method of modeling of uncertainty is preferable: random or fuzzy. Today both of these approaches are highly popular. Fuzzy and probabilistic approaches are commonly used for modeling of uncertainty. Fuzzy numbers can be used for modeling vagueness of parameters, such as risk-free rate or volatility in option pricing. Under these assumptions, option value depends on believe degree and turns to fuzzy number. In this paper the Black – Scholes formula and it’s modification for American option arbitrage-free value are used. Fuzzy representations of underlying asset price, volatility of asset price and risk-free rate are used as parameters. There is set of papers regarding fuzzy approach for European option pricing. In this paper fuzzy approach is used for arbitrage-free American option pricing for the first time. The fuzzy American call value is compared with fuzzy European option value.
Soft Computing (SC) is a consortium of fuzzy logic (FL), neurocomputing (NC), evolutionary computing (EC), probabilistic computing (PC), chaotic computing (CC) and parts of machine learning theory (ML). SC is the foundation for computational intelligence and is leading to the development of numerous hybrid intelligent information, control and decision-making systems. The methodology of computing with words (CW) is an important event in the evolution of cognitive science, natural language processing, artificial intelligence, and different existing scientific theories. This is because CW can enrich the existing scientific theories and the above-mentioned science fields giving them the capability of using natural languages to operate on perception-based information, not only measurement-based information. Indeed in many real-world problems in natural sciences as well as in industrial engineering, economics, and business, often there is a need to deal with both perception and measurement based information. In the case of perception based information, the available information is not precise enough to justify the use of numbers. Such information is usually described in natural languages rather than in strict (idealized) mathematical expressions. So a strong need has appeared for a new approach, theory and technology for the development of knowledge representation, computing, and reasoning tools that allow creation of systems with high MIQ. The sessions of the ICSCCW-2011 will focus on the development and application of Soft Computing technology and computing with words paradigm in system analysis, decision and control.
This volume contains papers presented at the 13th International Conference on Rough Sets, Fuzzy Sets and Granular Computing (RSFDGrC) held during June 25–27, 2011, at the National Research University Higher School of Economics (NRU HSE) in Moscow, Russia. RSFDGrC is a series of scientific events spanning the last 15 years. It investigates the meeting points among the four major disciplines outlined in its title, with respect to both foundations and applications. In 2011, RSFDGrC was co-organized with the 4th International Conference on Pattern Recognition and Machine Intelligence (PReMI), providing a great opportunity for multi-faceted interaction between scientists and practitioners. There were 83 paper submissions from over 20 countries. Each submission was reviewed by at least three Chairs or PC members.We accepted 34 regular papers (41%). In order to stimulate the exchange of research ideas, we also accepted 15 short papers. All 49 papers are distributed among 10 thematic sections of this volume. The conference program featured five invited talks given by Jiawei Han, Vladik Kreinovich, Guoyin Wang, Radim Belohlavek, and C.A. Murthy, as well as two tutorials given by Marcin Szczuka and Richard Jensen. Their corresponding papers and abstracts are gathered in the first two sections of this volume.
This paper presents the results of volatility forecasting for indices of the Russian stock market using existing and developed by the authors fuzzy asymmetric GARCH-models. These models consider various switching functions which are taking into account the positive and negative shocks and are built using the tools of fuzzy numbers. Furthermore, in some models there are used switching functions that consider expert macroeconomic information. It was shown that fuzzy asymmetric GARCH-models provide a more accurate prediction of volatility than similar crisp models.
The companies that are IT-industry leaders perform from several tens to several hundreds of projects simultaneously. The main problem is to decide whether the project is acceptable to the current strategic goals and resource limits of a company or not. This leads firms to an issue of a project portfolio selection; therefore, the challenge is to choose the subset of all projects which satisfy the strategic objectives of a company in the best way. In this present article we propose the multi-objective mathematical model of the project portfolio selection problem, defined on the fuzzy trapezoidal numbers. We provide an overview of methods for solving this problem, which are a branch and bound approach, an adaptive parameter variation scheme based on the epsilon-constraint method, ant colony optimization method and genetic algorithm. After analysis, we choose ant colony optimization method and SPEA II method, which is a modification of a genetic algorithm. We describe the implementation of these methods applied to the project portfolio selection problem. The ant colony optimization is based on the max min ant system with one pheromone structure and one ant colony. Three modification of our SPEA II implementation were considered. The first adaptation uses the binary tournament selection, while the second requires the rank selection method. The last one is based on another variant of generating initial population. The part of the population is generated by a non-random manner on the basis of solving a one-criterion optimization problem. This fact makes the population more strongly than an initial population, which is generated completely by random.
Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the more than 120 papers published between 2003 and 2011 on FCA with fuzzy attributes and rough FCA. We applied traditional FCA as a text-mining instrument to 1072 papers mentioning FCA in the abstract. These papers were formatted in pdf files and using a thesaurus with terms referring to research topics, we transformed them into concept lattices. These lattices were used to analyze and explore the most prominent research topics within the FCA with fuzzy attributes and rough FCA research communities. FCA turned out to be an ideal metatechnique for representing large volumes of unstructured texts.
Article considers theoretical prerequisites of creation of optimum hierarchical structure of system of monitoring of crucial parameters of food safety of Russia on the basis of application of the theory of indistinct sets.
The definition of a phoneme as a fuzzy set of minimal speech units from the model database is proposed. On the basis of this definition and the Kullback-Leibler minimum information discrimination principle the novel phoneme recognition algorithm has been developed as an enhancement of the phonetic decoding method. The experimental results in the problems of isolated vowels recognition and word recognition in Russian are presented. It is shown that the proposed method is characterized by the increase of recognition accuracy and reliability in comparison with the phonetic decoding method
The paper examines the structure, governance, and balance sheets of state-controlled banks in Russia, which accounted for over 55 percent of the total assets in the country's banking system in early 2012. The author offers a credible estimate of the size of the country's state banking sector by including banks that are indirectly owned by public organizations. Contrary to some predictions based on the theoretical literature on economic transition, he explains the relatively high profitability and efficiency of Russian state-controlled banks by pointing to their competitive position in such functions as acquisition and disposal of assets on behalf of the government. Also suggested in the paper is a different way of looking at market concentration in Russia (by consolidating the market shares of core state-controlled banks), which produces a picture of a more concentrated market than officially reported. Lastly, one of the author's interesting conclusions is that China provides a better benchmark than the formerly centrally planned economies of Central and Eastern Europe by which to assess the viability of state ownership of banks in Russia and to evaluate the country's banking sector.
The paper examines the principles for the supervision of financial conglomerates proposed by BCBS in the consultative document published in December 2011. Moreover, the article proposes a number of suggestions worked out by the authors within the HSE research team.