Description: This is a simplified approach to calculating the variance of the whole life random variable in certain, very common circumstances.

Description: A study of the effect of random interest rates on life insurance programs and on annuities both certain and non-certain. This is done under several assumptions on the stochastic structure of the interest rates.

Description: Sooner or later a casualty actuary is confronted by the question, Given a history of paid loss amounts by calendar year, what should reserves be? Often, it is not possible to accurately gather and analyze additional data within the time constraints for the reserving decision. The algebraic reserving method presented in this paper offers one approach to rapidly addressing this problem.

Description: The classical approach to life contingencies has treated actuarial functions as fixed quantities. In point of fact, these functions really represent the mean or expected values of random variables which are functions at the length of time to death of a life aged x. In this paper, we will present some examples of this approach. Talk given at the thirteenth annual Actuarial Research Conference held at Ball State University, Muncie, Indiana, September 1, 1978.

Description: In this expository paper several comments are made with respect to the statistical independence of the curtate future lifetime and the fractional part of the future lifetime, both of a general status. In particular, the conditions for independence need to be stated carefully. The last-survivor status is cited as an example. More general assumptions than the uniform distribution of deaths assumption are then considered, together with applications to insurances, annuities, and reserves. Similar results to those under the uniform distribution of deaths assumption are obtained. Brief comments are made with respect to contingent probabilities in multiple lives and multiple decrement theory.

Description: We apply decision theory to develop a credibility formula that minimizes a loss function that is a linear combination of a squared-error term and a second-derivative term. The squared-error term measures the accuracy of the estimator, while the second-derivative term constrains the estimator to be close to linear.

Description: In this paper,we present a method which first converges a two dimensional data to a univariate one and then uses the interval censoring technique to estimate the probability of failure of a Joint-life status from a heavily censored data. Our study shows that the life annuities of joint-life status calculated assuming independence overestimates the ones evaluated from an actual sample of population.

Description: This paper is to some extent a sequel to my previous paper A Bond Manager's Method for ALM published in Actuarial Research Clearing House Volume 1993.3. It borrows from that paper the concept of benchmark weights for measuring the sensitivity of the present value of a set of cash flows to changes in interest rates. However, a completely different approach to calculating benchmark weights is presented.

Description: The main objective of this study is to analyze and control a surplus dependent risk process, where larger surpluses allow for a wider underwriting policy. We focus here mostly on the diffusion approximation of the risk process. The results are derived in two papers Brownian motion in Risk Theory, submitted for publication, and Surplus dependent risk processes defined by stochastic differential equations, in preparation. We only include here a long summary of these papers.

Description: Sooner or later a casualty actuary is confronted by the question, Given a history of paid loss amounts by calendar year, what should reserves be? Often, it is not possible to accurately gather and analyze additional data within the time constraints for the reserving decision. The algebraic reserving method presented in this paper offers one approach to rapidly addressing this problem. The paper consists of four sections - General Considerations, Formulas, Examples, and Conclusion.