Description: In this note, we rearrange the statement and the proof of a theorem in Greville. The presentation appears to be more compact the materials, however, are not new.].

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: An insurance company starts with an initial surplus, collects premium, pays claims to policyholders and pays dividends to stockholders. What remains is the following year’s surplus. The process continues. This paper describes how to calculate the distribution of surplus for any given year. With these distributions, one can make the calculations of premiums and dividends.

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: 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 purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic i.e. non- stochastic framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.

Description: This paper discusses a problem in corporate finance, the problem of selecting from among a group of possible economic projects. This problem most certainly involves future contingent events and is a natural for consideration by actuaries interested in expanding into non-traditional practice areas.

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

Description: This paper considers the Bayesian analysis of the generalized Poisson distribution GPD and the generalized Poisson regression GPR model. Markov chain Monte Carlo MCMC methods and random variety generation strategies such as adaptive rejection sampling ARS for log-concave densities and adaptive rejection Metropolis sampling ARMS are discussed and then utilized in order to advance the Bayesian analysis of these generalized Poisson models.