Description: The objective of this paper is to present and to apply a numerical method in the calculation of the minimal and maximal ultimate ruin probabilities in two risk models given some moment constraints on the individual claimsize distribution. An application of this optimization problem is to find the extremal lower and upper bounds of the ultimate ruin probabilities given those constraints. The paper considers the classical risk models with constant and variable premiums.

Description: The dependent relationship between two lives is readily analyzed within the context of probability theory. This paper presents useful relationships between certain actuarial and probability functions and then explores measures of dependence. From Transactions of Society of Actuaries 1986, Vol. 38.

Description: This article provides an an alternate, statistical approach, to graduation. Both single and multiple decrement models are considered and theoretical results are obtained for some specific mortality models. From: ACTUARIAL RESEARCH CLEARING HOUSE, 1979 VOL. 2.

Description: In this paper, Lagrangian distributions are reviewed and some of their properties are studied. Recursive methods are proposed to calculate compound Lagrange distributions. Some examples for a sub-family of Lagrangian Distributions and its compound distributions are studied.

Description: This paper describes how Markov chain Monte Carlo and related methods recently presented in the statistical literature can be used to quickly and efficiently simulate random draws from distributions with log-concave or nearly log-concave densities. From Transactions of Society of Actuaries 1995, Vol. 47.

Description: 1996 Valuation Actuary Symposium. Topics discussed in this session included developing an approach to quantifying C-3 risk and exploring ways to improve the C-3 component of the NAIC RBC formula.

Description: Two-dimensional data can be smoothed by minimizing a combination of the sum of weighted absolute deviations from initial estimates and the sums of absolute values of differences in the two directions. This paper discusses the techniques of parametric programming which make it feasible to explore the different results obtained by varying the emphasis given to fit versus smoothness. From Actuarial Research Clearing House 1994, VOL. 1.

Description: This paper studies the joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. The classical model is generalized by discounting with respect to the time of ruin. The authors show how to calculate an expected discounted penalty, which is due at ruin, and may depend on the deficit at ruin and the surplus immediately before ruin.

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: 1988 Valuation Actuary Symposium. In this session the speaker described the modeling of the participating whole life division including the product description, modelling assumptions, operation of the model, and the results.