Description: Demography is a very exciting subject. With a simple mathematical model, students can project a country's population forward 25, 59, 75 even 100 years. This paper will focus on six ideas from demography. They all can be useful to an actuary, yet none of them would be considered at any length if the actuary didn’t study demography.

Description: The theory underlying the Moving Weighted Average graduation method is restated in the language of linear algebra which provides for an enrichment of the family of formulas. A comparison of the results of applying six members of the family to 100 simulated data sets is provided.

Description: The values of life insurance and annuity liabilities move in opposite directions in response to a change in the underlying mortality. Natural hedging utilizes this to stabilize aggregate liability cash flows. Our study shows empirical evidence that insurers who utilize natural hedging also charge lower premiums than otherwise similar insurers. This indicates that insurers who are able to utilize natural hedging have a competitive advantage. In addition, we show how a mortality swap might be used to provide the benefits of natural hedging to a firm that writes only one of the lines of business.

Description: This paper presents the modeling of mortality risk from exposure to a potential future extreme event such as a natural disaster and a terrorist attack, and its impact on life insurance. With this new model, quantities associated with the total force of mortality such as survival function are derived and the impact of mortality risk on life insurance is examined.

Description: As a life reinsurer, understanding mortality risk is mission critical. Superior models of mortality risk lead to more competitive pricing in profitable market segments and more efficient use of capital. Surprisingly, modern statistical tools such as predictive modeling have not previously been used to model mortality data to gain this edge. In this paper, we present the use of a predictive modeling technique called projection pursuit regression PPR to model mortality data. We first describe the process of creating a PPR model using inter-company mortality data collected by the Individual Life Experience Committee of the Society of Actuaries, and present the resulting model. We then discuss the process of using this model as a starting point for creating a more detailed PPR model of internal company mortality data.

Description: In this paper we shall present our results in terms of the estimation of human mortality rates, but the results carry over to other applications. We shall discuss a Bayesian model that encompasses both graduation [smoothing] and prediction.

Description: The Lee and Carter LC method is getting widely adopted for long-run forecasts of age specific mortality rates. That popularity is first due to the model simplicity. Moreover, the LC model has given successful results for various countries e.g. U.S., Chile, G7 countries. However, some difficulties arose when using population data from certain countries such as UK and Australia. In the present paper, the LC model is applied to data from four Nordic countries: Denmark, Finland, Norway and Sweden. The Singular Value Decomposition SVD, the Weighted Least Square WLS and the Maximum Likelihood estimate MLE are used. These approaches give satisfactory results. The appropriate fitting period needs, however, to be well chosen. The properties of the model's parameters are studied using a bootstrap simulation.

Description: Discussion on Living to 100 Session 4A. Papers presented: Inference for Logistic-type models for the Force of Mortality and, Predictive Modeling for Advanced Age Mortality

Description: This paper investigates the use of models of dependent mortality for determining annuity values. We discuss a broad class of parametric models using a bivariate survivorship function called a copula. Using data from a large insurance company to illustrate our methods, we calculate maximum likelihood estimates to calibrate the rnodel.

Description: We employ a framework for the classification of mortality evolution patterns to HMD data. We find both supra-regional patterns and outliers from global trends.