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: This paper presents a new methodology for obtaining fast algorithms and closed form solutions for pricing callable bonds in continuous time models. Results are directly applicable to regulatory scenario testing, immunization and market value accounting.

Description: This is authors' Fellowship Credit Research Paper. This paper will develop a model for cash flow testing traditional participating insurance that utilizes pricing tools and assumptions to project reserve liabilities. The model makes use of finance and accounting tools to monitor the reasonableness of ending and intermediate surplus results that emerge under the various interest rate scenarios imposed.

Description: During the last decade, a vast activity had been observed in generalizing of the classical discrete distributions. The main idea was to apply the extended versions fur modeling different kinds of dependent count or frequency data structure in various fields. In the present paper we suggest extensions of the classical univariate geometric, negative binomial, Poisson, Bernoulli, binomial and logarithmic series distributions, by including an additional parameter. It has a natural interpretation in terms of zero-inflation, and because of this we named the corresponding generalized versions adding inflated-parameter.

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: The purpose of this paper is to present to the actuarial profession a stochastic investment model which can be used for simulations extending for many years ahead. Discussed in the paper are the general reasons for choosing the style of model, the general model and how to use it, the assumptions and the sensitivity of model to the assumptions made and the possible applications in the investment and actuarial fields.

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.

Description: This paper shows how the results of copula based capital aggregation models can always be locally approximated by relatively simple formulas. The paper defines the concepts of diversification factor and tail correlation matrix and describes methods for estimating these quantities from simulated data. We show how these ideas can be put into practice as both computational shortcuts and presentation tools.

Description: In the copula literature there are many bivariate distribution families but very few higher dimensional ones. Moreover, most of these are difficult to work with. Some of the bivariate families can be extended to more dimensions but in general the construction of distribution functions with more than two variables is a difficult problem. This paper introduces a construction method that is straightforward to implement and can produce multivariate distribution functions of any dimension.

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.