Description: This paper thoroughly describes risk premium calculation based on an insurance portfolio consisting of policies risks insured over a finite time interval.

Description: This is a letter from Jan M. Hoem to Arnold F. Shapiro about Exposed-to-risk considerations based on the Balducci assumption and other assumptions in the analysis of mortality.

Description: This paper introduces a new direction for evaluating numerically survival probabilities pointed out by H. Seal in his book ‘Survival Probabilities: The goal of Risk Theory’. Some of special cases can be considered as a weighted Poisson process with an infinitely divisible mixing distribution. This property is well known for the negative binomial case [gamma mixing distribution].

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: A theoretical study of the interrelationship between the financial and insurance risk markets.

Description: Random sum models with compound distributions are used extensively in modeling of insurance risks. Unfortunately, the compound distributions themselves are awkward to evaluate. Consequently, various numerical and analytical approximative techniques have been used. In this talk we derive various upper and lower bounds on the tails of compound distributions. Some notions in reliability theory are used.

Description: The paper gives two criteria for fit and uses two different criteria to transform an initial graduation into one with better fit. It is shown that the two sets of criteria give the same transformation. The mathematical relationships between the two sets of criteria are then derived. It is clear from those relationships that when one set of criteria is small, the other set is small [but reasonably the same]. Some general comments on various measures of fit are made.

Description: This article investigates the simplicity of the Balducci hypothesis, and compares the fractional-age death probability given by three widely used assumptions: uniform distribution of deaths, the Balducci hypothesis, and constant force of mortality [1, 2].

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 investment risk generated by a stochastic interest rate is recognized as often the greatest risk associated with a whole life or retirement policy. Recent research has investigated the mathematics of this risk when the interest rate follows a stochastic process and the time to death is considered to be random. In this paper we focus on the use of the zero coupon bond as an investment instrument to fund a whole life policy. It is unlikely that a company will entirely fund a particular single policy with a zero coupon bond.