Description: In this paper, Bivariate Schuette graduation is applied to mortality rates among black male retired workers [Social Security data] at ages 70 to 83. Graduated values for various choices of the parameters are compared. The Schuette method is also adapted to calculate regression quantiles, providing upper and lower envelopes for the graduated values.

Description: The American Academy of Actuaries and the Society of Actuaries have joined resources to maintain this Economic Scenario Generators Excel Workbook tool for use in regulatory reserve and capital calculations. Please see the SOA website research pages for further information on this tool and how to use it.

Description: The Karup-King formula with equal intervals has an elegant symmetric structure providing for efficient calculation. This paper traces the algebra involved in a generalization of this formula to the case of unequal intervals. So far, this formula does not have an elegant structure. However, a degree of elegance can be obtained in terms of matrix notation which can readily be used with a computer language such as APL.

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: Up to now, the main aim of credibility theory has been to provide statistical models which allow for estimating [net] risk premiums appropriately. In this note, a simple credibility model based on the percentile principle is introduced. It turns out that there are close connections between the resulting credibility premiums and statistical tolerance limits.

Description: This paper investigates nonparametric estimators of the distribution function that are based on mixtures of gamma distributions when we have a random sample from a continuous distribution function. From Actuarial Research Clearing House 1993, VOL. 3.

Description: The theme of this presentation relates to solving portfolio selection problems using linear and fractional programming. Two key contributions: 1. Generalization of the CVaR linear optimization framework. 2. Equivalences among four formulations of Coherent Distortion Risk Mearures optimization problems. From Actuarial Research Clearing House, 2012, Vol. 1.

Description: We find the necessary and sufficient conditions for fitting five given moments by a triatomic distribution. We consider three examples drawn from fire large spread, individual life medium spread and group life small spread insurance data, fit them with triatomics, and compute the ruin probabilities using well known formulas for discrete and for combination of exponentials claim amounts. We then compare our approximations with the exact values that appeared in the literature.

Description: A short note on derivatives of decreasing life annuities that was motivated by Exercise 5.35 on page 156 of 'Actuarial Mathematics'. Actuarial Research Clearing House 1993 VOL. 2

Description: The MACRA/QPP Payer Revenue Model is designed to provide Health Plans an estimate of the expected claim cost increase/decrease due to MACRA.