Description: It is obvious that the introduction of a deductible has two major effects. The amount paid for every claim will drop, resulting in a lower claim burden for the insurance company. There will also be a drop in claim frequency, leading to a decrease in claim handling expenses. However, it is by no means obvious how the average claim size changes with the introduction of a deductible. In this paper, we will study this question. First, we derive some theoretical results then apply them to concrete distributions.

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: The article provides a complete and rigorous analysis based on calculus for the topics in the theory of compound interest: the monotone convergence properties of the rates of interest and discount payable m times per interest conversion period in relation to the force of interest, the monotone convergence properties of the present value and accumulated value of an ordinary annuity with m payments per interest conversion period in relation to those of a continuously paying ordinary annuity and a method for approximating the present value of an ordinary annuity, or an increasing annuity with m payments per interest conversion period, by accumulating, at compound interest for the fraction m - l/2m of an interest conversion period, the present value of the same type of annuity with one payment per interest conversion period.

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: In addition to death and maturity guarantees on the mutual funds they sell, some insurance companies make it possible for the investor to extend the guarantees for a fixed number of years. In this paper, we consider the case when that option is of the European type that is, the investor, at maturity, can either close out the contract or extend it for the stated, fixed term. When extended, the guarantee is on the value of the fund at the original maturity date. The fund is assumed to be fully invested in common stock.

Description: This paper develops a method for estimating the future claim costs of known ongoing large medical claims. It applies Least Squares analysis of historical experience to derive two arrays of factors. One array is to be applied as a vector inner product with claim costs already incurred and/or paid to project a total future claim cost. The second array distributes the total future claim cost over the months following the analysis date.

Description: The purpose of this note is to show how certain formulas of life contingencies can be derived almost painlessly under the uniform distribution of deaths assumption.

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: 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.