Mathematical methods for studying risks (resumptive article)

We define risk as an unwanted opportunity and divide risk theory into three stages — risk analysis, risk estimation, risk management. Safety and risk are directly related to each other, being like a «mirror image» of each other which necessitates developing both the general theory of risk and particular theories of risk in specific areas. General risk theory allows for a uniform approach to the analysis, estimation and management of risks in specific situations. Currently, three main approaches to accounting for the uncertainty and describing risks are used — probabilistic and statistical approach, fuzzy sets, and the approach based on interval mathematics. The methods of risk estimation primarily based on probabilistic and statistical models are considered. The mathematical apparatus for estimating and managing risks is based on nonparametric formulations, limit relations, and multi-criteria optimization. Asymptotic nonparametric point estimates and confidence limits for the probability of a risk event are constructed on the base of binomial distribution and the Poisson distribution. Rules for testing statistical hypotheses regarding the equality (or difference) of two probabilities of risk events are proposed. An additive-multiplicative risk estimation model based on a hierarchical risk system based on a three-level risk system has become widespread: private risks — group risks — final risk. For this model, the role of expert estimation is revealed. The prospects of using (in the future) the theory of fuzzy sets are shown. The article deals with the main components of the mathematical apparatus of the theory of risks, in particular, the mathematical support of private theories of risks related to the quality management, innovations and investments. The simplest risk assessment in a probabilistic-statistical model is the product of the probability of a risk event and the mathematical expectation of the accidental damage. Mathematical and instrumental methods for studying global economic and environmental risks are discussed.

An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data

In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family’s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, Rényi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family’s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fréchet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.

Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments

In this paper, we consider the sum Snξ = ξ1 + ... + ξn of possibly dependent and nonidentically distributed real-valued random variables ξ1, ... , ξn with consistently varying distributions. By assuming that collection {ξ1, ... , ξn} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for E((Snξ)α1(Snξ > x)) and E((Snξ – x)+)α, where α is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.

Study on the Staged Operation of a Multi-Purpose Reservoir in Flood Season and Its Effect Evaluation

A reasonable analysis of flood season staging is significant to the management of floods and the alleviation of water shortage. For this paper, the case of the Chengbi River Reservoir in China was selected for study. Based on fractal theory, the flood season is divided into several sub-seasons by using four indexes (multi-year average daily rainfall, multi-year maximum rainfall, multi-year average daily runoff, and multi-year maximum daily runoff) in this study. Also the Benefit-Risk theory is applied to evaluate the effects of staged dispatching. The results show that the flood season of the Chengbi River basin should be divided into the pre-flood season (13 April–6 June), the main flood season (7 June–9 September) and the post-flood season (10 September–31 October). After adjusting the flood limit water level for sub-season and benefit assessment, the probability of exceedance after reservoir flood season operation increases by 0.13×10-5, the average annual expected risk is 0.2264 million RMB, and the average annual benefit increases by 0.88–1.62 million RMB. The benefits obtained far outweigh the risks, indicating the importance of staging the flood season.

EXPERIENCE IN TRAINING PERSONNEL TO ENSURE THE COMPUTER SECURITY OF THE TRANSPORT INDUSTRY

In the context of the pandemic, the role of computer security specialists in solving the problems of uninterrupted operation of transport enterprises has increased many times. The article is devoted to summing up and analyzing the experience accumulated in the RUT (MIIT) for 20 years of training specialists in the specialty “Computer Security”, determining the prospects for the development of the educational program. The article presents a methodology for using freely distributed software created by the authors of the article in the learning process in cases where it is impossible or unsafe on real objects. The main advantage of this technique is that it takes into account the experience gained by specialists in solving real cases, allows you to reproduce real system vulnerabilities without harming real systems for training purposes, makes it possible to diagnose these vulnerabilities, exploit them, choose and compare different ways to remove them from the system. The article contains an analysis of publications devoted to the experience of training personnel in the specialty “Computer Security” in different countries using various tools. The article provides an overview of the educational program and formulates the principles that form the basis of training at our university, demonstrates examples of the use of digital doubles in the learning process, focuses on the formation of interdisciplinary con nections, skills of applying theoretical knowledge to solve practical problems and analyze the results obtained. The review of the subjects of the discipline “Methods of risk management analysis”, statistical analysis of the results of the implementation of the methodology developed by the authors in practice, and their graphical interpretation is carried out. Examples of the application of risk theory to solving computer security problems are given. The article contains examples of students ‘ participation in research activities, the creation of methodological support for the relevant educational program, and various events outside the university.