Description: The Lee and Carter LC method is getting widely adopted for long-run forecasts of age specific mortality rates. That popularity is first due to the model simplicity. Moreover, the LC model has given successful results for various countries e.g. U.S., Chile, G7 countries. However, some difficulties arose when using population data from certain countries such as UK and Australia. In the present paper, the LC model is applied to data from four Nordic countries: Denmark, Finland, Norway and Sweden. The Singular Value Decomposition SVD, the Weighted Least Square WLS and the Maximum Likelihood estimate MLE are used. These approaches give satisfactory results. The appropriate fitting period needs, however, to be well chosen. The properties of the model's parameters are studied using a bootstrap simulation.

Description: This paper examines the models underlying three of the most influential FAHP articles.

Description: Recent articles addressed the subject of fuzzy regression [FR] and the term structure of interest rates [TSIR]. Their approach relied on possibilistic regression. Although possibilistic regression has been used in many applications, it has a number of limitations, not the least of which is its nebulous relation to the least-squares concept. As an alternative to possibilistic regression, this paper uses fuzzy least square regression to investigate the TSIR.

Description: This paper addresses the fuzziness in regression models. The goal is to present a test procedure to explicitly examine whether an independent variable has a clear functional relationship with the dependent variable in a specific regression model, or whether their relationship is fuzzy. To this end, the authors interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. They then derive test distributions based on the null hypothesis that such spreads could have been obtained with data generated by a classical regression model with random errors. The analysis is presented in conceptual rather than technical terms.

Description: This introduction is followed by an overview of RA, which includes such things as the role of RA in ERM, the conceptualization of RA, and the role of FL as it relates to RA. We turn then to an overview of the FL methodology used in this study. The next three chapters are devoted to FL methodology as it relates to RA issues, and includes a discussion of FL modification of the risk matrix, FL modification of the Analytic Hierarchy Process, and the role of fuzzy optimization as it relates to RA. We turn then to examples of RAA-FL in the areas of operational risk, hazard risk, financial risk and strategic risk. This is followed by closing comments and observations. The study concludes with an annotated bibliography.

Description: This paper gives an overview of fuzzy optimization, presents applications of fuzzy optimization and investigates ways to extend the methodology to risk assessment.