The logical and probabilistic (LP) approach in development and use of risk models in banking and business with groups of incompatible events (GIE) is stated. The features of LP-models based on analogy of GIE and Bayes' formula and application of well-organized probabilistic risk polynomial, constructed on logical connections of events, are substantiated. The methods of identification of LP risk models with using of statistical data are described. The estimation of accuracy and stability of risk LP models and their comparison with other risk models and methods of classification was performed. The examples of estimation and analysis of risk with using of LP risk models are presented.

The methodological aspects of the scenario logic and probabilistic (LP) non-success risk management are considered, following from analysis of connections between management and risk, personals and risk, and from study of risk management at stages of design, test and operation of complex systems.
The theoretical bases of the scenario non-success risk LP-management in business and engineering are stated, including LP-calculus, LP-methods, and LP-theory with groups of incompatible events (GIE). Examples of risk LP-models with logical connections OR, AND, NOT, cycles and GIE are given. Methods and algorithms for the scenario risk LP-management in problems of classification, investment and effectiveness are described.
Risk LP-models and results of numerical investigations for credit risks, risk of frauds, security portfolio risk, risk in quality, accuracy, and risk in multi-state system reliability are given. A rather large number of new problems of estimation, analysis and management of risk are considered. In some problems the risk LP-models prove to be showed almost two times more accurate, seven times more robustness and bigger transparency, than other well-known models of risks. Software for risk problems based on LP-methods, LP-theory with GIE and cortege algebra, is described too.
The book is intended for experts and scientists in the area of the risk in business and engineering, in problems of classification, investment and effectiveness, and students and post-graduates.

The problem of transparency of methods for estimation of credit risk for natural and juridical persons is formulated and its solution, based on logical and probabilistic (LP) approach, is suggested. We study Basel II Regulations about minimum capital requirements and describe the difficulties of their implementation due to the absence of effective transparent methodologies for estimation of credit risks. The LP-theory of credit risk with groups of incompatible events is stated. We demonstrate advantages of the LP-theory of risk in transparency, accuracy and robustness. LP-theory (LP- VaR) of the portfolio, using arbitrary distributions of dividend yields and providing transparency of analysis and risk forecasting, is stated. We conclude that Russian banks have to found their own rating agency on the basis of impartial and well-grounded scientific LP-theory of credit risk. This book is intended for specialists in the area of risk management in banking and business, for students and postgraduates of financial universities.