Description: In the present paper, we propose and investigate a numerical method of computing the probability distribution of S. Inversion of the Laplace transform moment generating function is shown to be a better approach than the existing recursive method for find the distribution of sum of several independent random variables. In the continuous case, in many situations, numerical inversion needs to be used to compute the probability distribution function of the sum.

Description: The two-parameter Pareto distribution is a commonly used model in reliability and risk modeling. Minimum variance unbiased estimates of the parameters of Pareto distribution are not known. In this paper, we propose and investigate a method of estimation of the parameters of the Pareto distribution. This method is based on minimization of the Kolmogorov-Smirnov distance between the empirical cumulative distribution function [cdf] and the cdf of the Pareto distribution.

Description: This dialogue discusses the history and purpose of section 811(a) and its historic role in the computation of life insurance company taxable income and, in particular, reserves.

Description: This is a sequel to author's earlier paper on Installment Premiums. This paper explores the parallel case of apportionable premiums, another situation in which a special adjustment payment at death causes an otherwise somewhat complex policy to be identical with a more simple and familiar one. As with installment premiums, this will result in terminal reserves for the complex policy being exactly equal to those for its corresponding familiar policy.

Description: It has been twenty years since DeWit 1982 first applied fuzzy logic FL to insurance. That article sought to quantify the fuzziness in underwriting. Since then, the universe of discourse has expanded considerably and now the FL methodologies include used fuzzy set theory, fuzzy numbers and fuzzy arithmetic, fuzzy inference systems, fuzzy clustering algorithms, fuzzy linear programming, fuzzy regression, and hybrids involving other soft computing technologies. This article presents an overview of these studies.

Description: Panel discussion focused on the Effective Use of Capital. Topics included: 1. Definition of capital 2. Appropriate level of capital and surplus in a life insurance company 3. Alternatives for deploying capital 4. Returns a life company should demand on invested capital 5. How much a company should charge for lending its capital in reinsurance transactions

Description: Investment Fallacies: Gambler’s Fallacy: Probability of Reversion

Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

Description: These are the abstract and reference of the paper 'Bounds on Multiple Contingent Claims'. Lo considered the problem on bounding a European option on a single asset. He obtained an upper bound on the payoff of the European call in terms of the mean and variance of the underlying asset. In this talk, we extend Lo's result to the multi-asset case. Unlike the one asset case, the correlations between the assets play an important role and have to be taken into consideration.

Description: This is a letter from F.G. Reynolds, University of Waterloo, to Mr. C. Smith, Cologne Life Reinsurance Co. As an assignment the author had the students in his Risk Theory class extend the method of Trobliger to three levels of risk. Both the data of Trobliger and the data of Thyrion, which can be found on pages 27 and 16 of Seal's Stochastic Theory of a Risk Business, were fitted.