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This second edition of Mathematical Models of Financial Derivatives, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. It presents a self-contained treatment of risk-neutral valuation theory, martingale measure, and tools in stochastic calculus required for the understanding of option pricing theory. Derivative pricing models are solved using various approaches, by martingale pricing theory and partial differential equation methods. This text is targeted to students in mathematical finance. It also serves as a good reference for quantitative analysts and derivative traders in investment banks. The most recent research results and methodologies are made accessible to the reader through the extensive set of exercises at the end of each chapter.

In this article, relevant approaches to creating and using mathematical models in linguistics are examined. Analyzed are the types of mathematical methods used to solve linguistic tasks. Also investigated are the fundamental principles for creating mathematical models. Stressed in particular is that the approach usually applied in solving physical tasks can be effective. Its typical feature is that a universal theory explaining the interaction among a system's functional elements on the most general level is the basis of the model. In this case, the necessary approximating dependencies are not conjectured, as is often the case, but obtained or calculated on the basis of the fundamental theory. The prospects for applying this approach in linguistics are defined. Examples of the modeling of linguistic systems and a comparative analysis of their various methods are provided. Much attention is paid to the universality of the mathematical models used to analyze linguistic material. It is noted that if the approximate dependencies used are based on a system's general universal properties, this can significantly complicate the quantitative analysis of the data. The advantages and shortcomings of mathematical modeling in solving applied linguistic tasks are illustrated. Besides "classic" models (such as Zipf's law for the rank distribution of words in a text), other modeling approaches are described. In particular, attention is paid to the methods of constructing mathematical models based on neural networks. In this case, the approximation of dependence is realized in the form of sequential essentially nonlinear transformations. The main disadvantage of this approach is connected with the technical complications of execution and with the absence of overt analytical dependence. The main advantage is hidden in the potential possibility of creating approximate dependencies of practically any type. As a comparison of various modeling approaches, the article provides examples of solving the same linguistic tasks using several methods.

Theoretical basis for presenting research results in agricultural science is mathematical statistics and probability theory using empirical forms of generalization of experimental data. To improve the methods of planning field experiment and processing its data using digital technologies, we proposed to use mathematical modeling based on physical principle of balance of cause-and-effect interactions in a closed physical system as a priority option. When analyzing impact of environmental factors on crop yields, the initial provisions, the mathematical modeling of the crop yield is based, on are not associated with characteristics of crops and natural conditions, therefore, the model options are universal in application and are valid for any agricultural crop, regardless of the region of cultivation. To ensure statistically correct digital information, based on the established forms of mathematical model, the field experiment layout aimed at establishing the dependence of the crop yield on yield-forming factors should include at least 4 options for nutritional levels (NPK) with a research duration of at least 4 years. To check the accuracy of the developed crop yield model, the data of independent field experiments of Professor N.N. Semenenko with barley and winter triticale has been used. It has been determined that, in Belarus, yield-forming factors, as a result of their impact on the grain yield, are arranged in the following decreasing sequence: total dose of applied NPK º the amount of precipitation during the active phases of growing season → air temperature for the same period. Calculations have shown that decrease in the number of yield-forming factors taken into account in the mathematical model from three (food, moisture and heat) to two (food and moisture) reduces the accuracy of calculating the grain crop yield insignificantly.

An integrated set of mathematical models has been developed for use in the identification and quantitative measurement of logistics problems, and the prediction of probable results of proposed changes or corrective actions. The models can be used individually or in various combinations. Used together, they provide the logistics planner with a means for making a complete analysis of requirements for logistics and operations during any phase of a weapon system program.