This book offers a comprehensive guide to the modelling of operational risk using possibility theory. It provides a set of methods for measuring operational risks under a certain degree of vagueness and impreciseness, as encountered in real-life data. It shows how possibility theory and indeterminate uncertainty-encompassing degrees of belief can be applied in analysing the risk function, and describes the parametric g-and-h distribution associated with extreme value theory as an interesting candidate in this regard. The book offers a complete assessment of fuzzy methods for determining both value at risk (VaR) and subjective value at risk (SVaR), together with a stability estimation of VaR and SVaR. Based on the simulation studies and case studies reported on here, the possibilistic quantification of risk performs consistently better than the probabilistic model. Risk is evaluated by integrating two fuzzy techniques: the fuzzy analytic hierarchy process and the fuzzy extension of techniques for order preference by similarity to the ideal solution. Because of its specialized content, it is primarily intended for postgraduates and researchers with a basic knowledge of algebra and calculus, and can be used as reference guide for research-level courses on fuzzy sets, possibility theory and mathematical finance. The book also offers a useful source of information for banking and finance professionals investigating different risk-related aspects.

This book proposes complex hierarchical deep architectures (HDA) for predicting bankruptcy, a topical issue for business and corporate institutions that in the past has been tackled using statistical, market-based and machine-intelligence prediction models. The HDA are formed through fuzzy rough tensor deep staking networks (FRTDSN) with structured, hierarchical rough Bayesian (HRB) models. FRTDSN is formalized through TDSN and fuzzy rough sets, and HRB is formed by incorporating probabilistic rough sets in structured hierarchical Bayesian model. Then FRTDSN is integrated with HRB to form the compound FRTDSN-HRB model. HRB enhances the prediction accuracy of FRTDSN-HRB model. The experimental datasets are adopted from Korean construction companies and American and European non-financial companies, and the research presented focuses on the impact of choice of cut-off points, sampling procedures and business cycle on the accuracy of bankruptcy prediction models.

The bookalso highlights the fact that misclassification can result in erroneous predictions leading to prohibitive costs to investors and the economy, and shows that choice of cut-off point and sampling procedures affect rankings of various models. It also suggests that empirical cut-off points estimated from training samples result in the lowest misclassification costs for all the models. The book confirms that FRTDSN-HRB achieves superior performance compared to other statistical and soft-computing models. The experimental results are given in terms of several important statistical parameters revolving different business cycles and sub-cycles for the datasets considered and are of immense benefit to researchers working in this area.

This book offers a comprehensive guide to the modelling of operational risk using possibility theory. It provides a set of methods for measuring operational risks under a certain degree of vagueness and impreciseness, as encountered in real-life data. It shows how possibility theory and indeterminate uncertainty-encompassing degrees of belief can be applied in analysing the risk function, and describes the parametric g-and-h distribution associated with extreme value theory as an interesting candidate in this regard. The book offers a complete assessment of fuzzy methods for determining both value at risk (VaR) and subjective value at risk (SVaR), together with a stability estimation of VaR and SVaR. Based on the simulation studies and case studies reported on here, the possibilistic quantification of risk performs consistently better than the probabilistic model. Risk is evaluated by integrating two fuzzy techniques: the fuzzy analytic hierarchy process and the fuzzy extension of techniques for order preference by similarity to the ideal solution. Because of its specialized content, it is primarily intended for postgraduates and researchers with a basic knowledge of algebra and calculus, and can be used as reference guide for research-level courses on fuzzy sets, possibility theory and mathematical finance. The book also offers a useful source of information for banking and finance professionals investigating different risk-related aspects.

This book proposes complex hierarchical deep architectures (HDA) for predicting bankruptcy, a topical issue for business and corporate institutions that in the past has been tackled using statistical, market-based and machine-intelligence prediction models. The HDA are formed through fuzzy rough tensor deep staking networks (FRTDSN) with structured, hierarchical rough Bayesian (HRB) models. FRTDSN is formalized through TDSN and fuzzy rough sets, and HRB is formed by incorporating probabilistic rough sets in structured hierarchical Bayesian model. Then FRTDSN is integrated with HRB to form the compound FRTDSN-HRB model. HRB enhances the prediction accuracy of FRTDSN-HRB model. The experimental datasets are adopted from Korean construction companies and American and European non-financial companies, and the research presented focuses on the impact of choice of cut-off points, sampling procedures and business cycle on the accuracy of bankruptcy prediction models.

The bookalso highlights the fact that misclassification can result in erroneous predictions leading to prohibitive costs to investors and the economy, and shows that choice of cut-off point and sampling procedures affect rankings of various models. It also suggests that empirical cut-off points estimated from training samples result in the lowest misclassification costs for all the models. The book confirms that FRTDSN-HRB achieves superior performance compared to other statistical and soft-computing models. The experimental results are given in terms of several important statistical parameters revolving different business cycles and sub-cycles for the datasets considered and are of immense benefit to researchers working in this area.