Description: We provide a possible solution to deal with the parameter estimation of mortality models when the population size is small, based on graduation methods.

Description: Exam study notes on credibility theory.

Description: In this paper, we study a survival regression model known as Cox's proportional Hazards model. We assume that the data available are already grouped and develop a minimum distance estimation procedure that is also applicable when the data are also left or right censored. Asymptotic properties of the estimators are established and the numerical implementation of the method based on an iterated reweighted least squares algorithm is discussed.

Description: We apply decision theory to develop a credibility formula that minimizes a loss function that is a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear.

Description: By necessity, attributions of financial processes require approximations. Tools used for approximations include Aumann-Shapley, time step, step-through, average step-through, partial derivative, and average partial derivative. Significantly non-linear paths can cause problems during attribution. Time (theta) and market factors must be handled concurrently. Typically contractual factors can be handled separately. Average Step-Through, Aumann-Shapley and Aumann-Shapley-3 points perform the best given the same time period. Attribution should be done with fairly small time steps as opposed to using a lot of points in the Aumann-Shapley calculation, but using Aumann-Shapley-3 points as a last step has some advantages.

Description: This paper develops the formula for estimation of multivariate copula. These results can be applied to the estimation of correlation coefficients. From the Actuarial Research Clearing House 1994 Vol. 2 .

Description: This paper develops a method for estimating the future claim costs of known ongoing large medical claims. It applies Least Squares analysis of historical experience to derive two arrays of factors. One array is to be applied as a vector inner product with claim costs already incurred and/or paid to project a total future claim cost. The second array distributes the total future claim cost over the months following the analysis date.

Description: This paper suggests a possible flexible solution to the time and resource problems of running a large number of stochastic interest rate scenarios, by selecting a representative subset. Each interest rate scenario consists of 30 future spot yield curves, where a reasonable number of points are specified on each curve such as 12. The distribution of the scenarios is approximated by the subset and each scenario in the subset has equal weight. The method is independent of the interest rate generator used.

Description: Feature article about the use of approximations.

Description: Article from The Actuary, October 1985 – Volume No. 19, Issue No. 8 that talks about the Rule of 72.