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 demonstrates that the variance of the loss function for n-year term is greater than the sum of the variances of the loss functions for n-year pure endowment and n-year regular endowment plans. The result is true for both single premiums and annual premium plans.

Description: In the context of insurance economics, the PH-transform is justified through some basic postulates on market premiums. In this paper the PH-transform is applied to the present value random variable in life insurance and annuities. It provides an alternative to the commonly used equivalence principle in life insurance and annuities premium calculation. This research project is sponsored by a joint AERF/CKER Grant of the Society of Actuaries.

Description: This paper builds a new risk model for a firm which is sensitive to its credit quality. A modified Jarrow, Lando and Turnball model [Markov Chain model] is used to model the credit rating. Recursive equations for finite time ruin probability and distribution of ruin time are derived. Coupled Volterra type integral equation systems for ultimate ruin probability, severity of ruin and joint distribution of surplus before and after ruin are also obtained. Some numerical results are included.

Description: Statistical properties of interest, annuity and insurance functions are examined when mortality and interest are treated as having a random component. Several special models of interest rate fluctuation are examined in detail. It is hoped that such theory will be useful in developing fluctuation reserves and premium margins. Presented at the 13th Annual Actuarial Research Conference, Ball State University, August 31st. September lst, 2nd. 1978.

Description: Non-consequentiality is quite consequential for the claims made for the applicability of Risk Theory RT to decision problems that are not transparently tactical or wholly instrumental. On the negative side, RT is not normative or even a complete heuristic in such contexts. The author takes strong exception to the common tendencies, A to link risk theory with welfarism and versions of utilitarianism, and B to claim that with or without but especially with such linkage RT is normative in both moral and rational analysis, choice and action.

Description: This is the abstract of the paper Risk Classification by Fuzzy Cluster. In this paper an algorithm for risk classification is proposed. This algorithm is based on the concepts of fuzzy cluster. We test our algorithm with two examples, the results are very promising.

Description: The concept of transformed distributions is generalized in this paper. First the concepts of net premium intensity, loaded premium intensity and load generators arc introduced. Then transformed distributions are identified with premium intensity and hence the loaded premium is calculated from transformed distributions. Finally it is shown that this method of premimn calculation is arbitrage free and it incorporates the strengths of the utility approach.