"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

Application of the American Real Flexible Switch Options Methodology A Generalized Approach

The paper deals with the inclusion of flexibility in financial decision-making under risk. It describes the application of the real options methodology with the possibility of sequential multinomial decision-making. The basic intention is to describe and apply a generalized approach and methodology of the flexibility modeling and valuation based on multiple choices and non-symmetrical switching costs under risk. The stochastic dynamic Bellman optimization principle is explained and applied. The optimization criterion of the present expected value is derived and used. Likewise, an option valuation approach based on replication strategy and risk-neutral probability is applied. An illustrative example of the application of the real multinomial flexible non-symmetrical switch options methodology is presented for three chosen modes. The option flexible values are computed. The usefulness, effectiveness, and suitability of applying the generalized flexibility model in company valuation and project evaluation is verified and confirmed. The significance of applying the generalized methodology in transition market economies is discussed and verified.financial options; real options; Discrete Binomial Model; pricing; stochastic dynamic Bellman Optimization Principle; switch options

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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