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: A European call option pricing model similar to the Black-Scholes equation [1] is derived. Like the Black-Scholes equation, the model is based upon an assumption of a lognormal distribution of the price of a risky, non-dividend-paying security at a given point in the future. However, unlike Black-Scholes, the market's risk preference is recognized through a parameter that permits refinement of the model to agree either with experience or with future advances in the underlying theory.

Description: This paper develops credibility using a longitudinal data framework. In a longitudinal data framework, one might encounter data from a cross-section of risk classes towns with a history of insurance claims available for each risk class. For the marginal claims distributions, we use generalized linear models, an extension of linear regression that also encompasses Weibull and Gamma regressions. Copulas are used to model the dependencies over time specifically, this paper is the first to propose using a t-copula in the context of generalized linear models. The t-copula is the copula associated with the multivariate t-distribution like univariate t-distributions, it seems especially suitable for empirical work. Moreover, we show that the t-copula gives rise to easily computable predictive distributions that we use to generate credibility predictors. Like Bayesian methods, our copula credibility prediction methods allow us to provide an entire distribution of predicted claims, not just a point prediction.

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 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: This paper examines some new Bayesian models for loss reserving inspired by a consideration of some of the methods and techniques appearing in the traditional chain ladder literature. This includes a possibly order restricted hierarchical Bayesian model for the year over year development factors. The issues of reserve variability and ranges of reasonable reserve estimates are considered. A new Bornhuetter-Ferguson styled Bayesian method of estimate revision is also discussed. These Bayesian models can be implemented using Markov chain Monte Carlo MCMC methods in a variety of programming languages, and can serve as starting points for more advanced models. This paper describes their implementation in WinBUGS a specialized software program for MCMC simulations. Illustrative WinBUGS code is included.

Description: This paper, originally published in 1992 in the Transactions of Society of Actuaries Vol. 44, deals with a topic that is becoming increasingly important to actuaries in most fields of practice. “Without relying on formulas, this paper presents the important concepts underlying the theory of arbitrage-free pricing of interest-rate-contingent cash flows.” This paper, by James A. Tilley, won the 1992-93 Annual Prize, and the Halmstad Prize for 1992. The paper includes written discussion and the author’s review of the discussions.

Description: In this paper, we introduce a family of leptokurtic symmetric distributions represented by the difference of two gamma variates. Properties of this family are discussed. The Laplace, sums of Laplace and normal distributions all arise as special cases of this family. We propose a two-step method for fitting data to this family. We develop a statistical test for goodness-of-fit and introduce a test of normality of the data. A simulation study is provided to illustrate the theory.

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.