Description: A fuzzy random variable [FRV] has been conceptualized as a vague perception of a crisp but unobservable random variable [RV] and also as a random fuzzy set. Since actuaries seem receptive to these notions of FRV, and there are sources of uncertainty that RVs can not accommodate, but FRVs can, one would expect FRVs to be a component of the actuarial arsenal, but generally this is not the case. Assuming that the reason for this is that potential users are not sufficiently familiar with FRV methodology, the purpose of this article is to help alleviate this situation by presenting a FRV primer.

Description: In the classical risk theoretic model with Poisson claim arrival and exponential claims, consider the discounted value of claims nos. 3, 6, 9, and so on. [To risk theory specialists, considering every third claim in a Poisson arrival process is the same as assuming waiting times are Erlang[3] in a Sparre-Andersen model.] The distribution of the discounted value of future claims can be found. It turns out that this is the same as the distribution of the product of two independent variables, one having a gamma distribution, the other a 'complex-parameter beta product distribution'. The latter will be defined, it involves extending the usual beta distribution.

Description: This tool created graphs of Google's mobility Data. This version of the tool contains global, country-level data through July 31, 2020

Description: This paper explores areas where fuzzy logic models may be applied to improve risk assessment and risk decision-making. It discusses the methodology, framework and process of using fuzzy logic systems for risk management. With the help of practical examples, it is hoped that it will encourage wise application of fuzzy logic models to risk modeling.

Description: Authored by a MIB Solutions team of Tom Rhodes, Stuart Klugman, Marianne Purushotham and Stacy Gill, the report summarizes the results of a study on the application and adoption of credibility theory within the life insurance and annuity industry. In addition to the report, numerical examples related to the application of credibility to company mortality and lapse data are provided in the four Excel files. This excel spreadsheet is a numerical example relating to the application of Credibility for lapses by policy for limited fluctuation. Please see the SOA website research section for the full report on Credibility Theory Practices.

Description: This report describes a simple way to construct a bivariate copula with specified marginals and partially specified dependence. For example, the method allows one to model tail behavior scenarios while holding the core of the joint distribution fixed. An Excel workbook named CopulaExample.xls is provided to illustrate the method, including its use in Monte Carlo simulation.

Description: Life insurance industry use experience studies to manage and monitor their blocks of business. The purpose of this paper is to provide an overview of the data cleansing and validation role specific to the life insurance experience study process.

Description: This research report is a summary of an online survey and follow-up discussions with survey respondents on the current state of actuarial modeling controls within U. S. and Canadian life insurance and annuity companies. The current state was then compared to the results from the 2012 survey on this topic to examine the evolution in actuarial model controls and governance. The report also provides an industry assessment and proposes considerations for enhancing the current state towards a well-controlled governance framework.

Description: The Product Development Section, the Financial Reporting Section, the Modeling Section and the Committee on Life Insurance Research are pleased to present new research on modeling and forecasting cause-of-death mortality. Authored by a Milliman team led by Alexandre Boumezoued, the report develops a framework for forecasting cause specific death rates. Included also is a Cause of Deaths Forecasting Tool and a user guide for the tool.

Description: This presentation discussed the Copula Methodology, which is the most popular methodology in multivariate modeling in finance and insurance. The definition, advantages, limitations, and uses of the Copula Methodology were presented. Some other multivariate models were discussed as well. From Actuarial Research Clearing House, 2012, Vol. 1.